Inner radius of cylindrical pipe r = 24/2 = 12 cm, outer radius R = 28/2 = 14 cm and lenght h = 35 m Volume of cylindrical wooden pipe = π(R² - r²)h = 22/7 × (14² - 12²) × 35 = 22 × (196 - 144 ) × 5 = 22 × 52 × 5 = 5720 cm³ Mass of cylindrical wooden pipe = 5720 × 0.6 g = 3432 g = 3.432 kg [∵ 1 cm³Read more
Inner radius of cylindrical pipe r = 24/2 = 12 cm, outer radius R = 28/2 = 14 cm and lenght h = 35 m
Volume of cylindrical wooden pipe = π(R² – r²)h
= 22/7 × (14² – 12²) × 35 = 22 × (196 – 144 ) × 5 = 22 × 52 × 5 = 5720 cm³
Mass of cylindrical wooden pipe = 5720 × 0.6 g = 3432 g = 3.432 kg [∵ 1 cm³ of wood has a mass of 0.6 g]
Hence, the volume of cylindrical wooden pipe is 3.432 kg.
Length of tin can l = 5 cm, breadth b = 4 cm and height h = 15 cm Volume of tin can = lbh = 5 × 4 × 15 = 300 cm³ Radius of plastic cylinder r = 7/2 = 3.5 cm and height H = 10 cm Volume of plastic cylinder = πr²H 22/7 × 3.5 × 3.5 × 10 = 22 × 0.5 × 3.5 × 10 = 385 cm³ Difference between capacities of tRead more
Length of tin can l = 5 cm, breadth b = 4 cm and height h = 15 cm
Volume of tin can = lbh = 5 × 4 × 15 = 300 cm³
Radius of plastic cylinder r = 7/2 = 3.5 cm and height H = 10 cm
Volume of plastic cylinder = πr²H
22/7 × 3.5 × 3.5 × 10 = 22 × 0.5 × 3.5 × 10 = 385 cm³
Difference between capacities of two packs = 385 – 300 = 85 cm³
Hence, the capacity of plastic cylindrical pack is greater than tin can by 85 cm³.
(I) Lateral surface area of cylinder C = 94.2 cm² and height h = 5 cm. Let, the radius of cylinder = r cm Lateral surface area of cylinder C = 2πrh ⇒ 94.2 = 2 × 3.14 × r × 5 ⇒ r = (94.2)/(3.14×10) = 3 cm Hence, the radius of base is 3 cm. (II) Volume of cylinder = πr²h = 3.14 × 3 × 3 × 5 = 141.3 cm³Read more
(I) Lateral surface area of cylinder C = 94.2 cm² and height h = 5 cm.
Let, the radius of cylinder = r cm
Lateral surface area of cylinder C = 2πrh
⇒ 94.2 = 2 × 3.14 × r × 5 ⇒ r = (94.2)/(3.14×10) = 3 cm
Hence, the radius of base is 3 cm.
(II) Volume of cylinder = πr²h = 3.14 × 3 × 3 × 5 = 141.3 cm³
Hence, the volume of cylinder is 141.3 cm³.
(I) Cost of painting the inner curved surface of cylindrical vessel = Rs 2200 and height h = 10 m. Let, the inner radius of cylindrical vessel = r m The inner curved surface area of cylindrical vessel = 2πrh The cost of painting is at the rate of Rs 20 per m² = Rs 20 × 2πrh According to question, RsRead more
(I) Cost of painting the inner curved surface of cylindrical vessel = Rs 2200 and height h = 10 m.
Let, the inner radius of cylindrical vessel = r m
The inner curved surface area of cylindrical vessel = 2πrh
The cost of painting is at the rate of Rs 20 per m² = Rs 20 × 2πrh
According to question, Rs 20 × 2πrh = 2200
⇒ 2πrh = 2200/20 = 110
Hence, the inner curved surface area is 110 m².
(II) The inner curved surface area of cylindrical vessel = 2πrh
⇒ 110 = 2 × 22/7 × r × 10 ⇒ r = 110×7/22×2×10 = 7/4 = 1.75 m
Hence, the radius of base of cylindrical vessel is 1.75 m.
(III) Volume of cylindrical cessel = πr²h
= 22/7 × 1.75 × 1.75 × 10 = 22 × 0.25 × 1.75 × 10 = 96.25 m³
Hence, the volume of cylindrical vessel is 96.25 m³.
Capacity of cylindrical vessel V = 15.4 litres = 15.4/1000m³ = 0.0154 m³ and height h = 1 m Let, the radius of cylindrical vessel = r m Volume of cylindrical vessel V = πr²h ⇒ 0.0154 = 22/7 r²× 1 ⇒ r² = 0.0154 × 7/22 = 0.0049 ⇒ r = √0.0049 = 0.07 m Total surface area of cylindrical vessel = 2πr(r +hRead more
Capacity of cylindrical vessel V = 15.4 litres = 15.4/1000m³ = 0.0154 m³ and height h = 1 m
Let, the radius of cylindrical vessel = r m
Volume of cylindrical vessel V = πr²h
⇒ 0.0154 = 22/7 r²× 1
⇒ r² = 0.0154 × 7/22 = 0.0049
⇒ r = √0.0049 = 0.07 m
Total surface area of cylindrical vessel = 2πr(r +h)
= 2 × 22/7 × 0.07 × (0.07 + 1) = 2 × 22 × 0.01 × 1.07 = 0.4708 m²
Hence, 0.4708 m² metal sheet is required to make this cylindrical vessel.
Radis of sphere r = 10.5 cm Surface area of sphere = 4πr² = 4 × 22/7 × 10.5 × 10.5 = 4 × 22 × 1.5 × 10.5 = 1386.00 cm² Hence, the surface area of sphere is 1386 cm²
Radis of sphere r = 10.5 cm
Surface area of sphere = 4πr²
= 4 × 22/7 × 10.5 × 10.5 = 4 × 22 × 1.5 × 10.5 = 1386.00 cm²
Hence, the surface area of sphere is 1386 cm²
Speed of river l = 2 Km/h = 2000 m/h, breadth b = 40 m and height h = 15 m Volume of water fall into the sea in 1 hour = lbh = 2000 × 40 × 3 = 240000 m³ So, volume of water fall into the sea in 1 minute = 240000m³/60 = 4000 m³ Hence, in 1 minute, 4000 m³ will fall into the sea.
Speed of river l = 2 Km/h = 2000 m/h, breadth b = 40 m and height h = 15 m
Volume of water fall into the sea in 1 hour = lbh = 2000 × 40 × 3 = 240000 m³
So, volume of water fall into the sea in 1 minute = 240000m³/60 = 4000 m³
Hence, in 1 minute, 4000 m³ will fall into the sea.
First case: Radius of balloon r = 7 cm Surface area of balloon = 4πr² = 4 × 22/7 × 7 × 7 = 4 × 22 × 7 = 616 cm² Hence, the surface area of ballon is 616 cm² Second case: Radius of balloon R = 14 cm Surface area of bolloon = 4πR² = 4 × 22/7 × 14 × 14 = 4 × 22 × 2 × 14 = 2464 cm² Hence, the surface arRead more
First case:
Radius of balloon r = 7 cm
Surface area of balloon = 4πr²
= 4 × 22/7 × 7 × 7 = 4 × 22 × 7 = 616 cm²
Hence, the surface area of ballon is 616 cm²
Second case:
Radius of balloon R = 14 cm
Surface area of bolloon = 4πR²
= 4 × 22/7 × 14 × 14
= 4 × 22 × 2 × 14
= 2464 cm²
Hence, the surface area of balloon is 2464 cm².
Ratio of surface area = 616/2464 = 1/4
Hence, the ratio of surface areas in two cases is 1:4
Length of water tank l = 6 m, breadth b = 5 m and height h = 4.5 m Volume of water tank = lbh = 6 × 5 × 4.5 = 135 cm³ = 135 × 1000 l = 135000 l Hence, the water tank can hold 135000 litres of water.
Length of water tank l = 6 m, breadth b = 5 m and height h = 4.5 m
Volume of water tank = lbh = 6 × 5 × 4.5 = 135 cm³ = 135 × 1000 l = 135000 l
Hence, the water tank can hold 135000 litres of water.
Length of cuboidal vessel l = 10 m, breadth b = 8 m and volume V = 380 m³ Let, the heigth of cuboidal vessel = h m Volume of cuboidal vessel = lbh ⇒ 380 = 10 × 8 × h ⇒ h = 380/(10×8) = 4.75 m Hence, the height of cuboidal vessel be 4.75 m.
Length of cuboidal vessel l = 10 m, breadth b = 8 m and volume V = 380 m³
Let, the heigth of cuboidal vessel = h m
Volume of cuboidal vessel = lbh
⇒ 380 = 10 × 8 × h
⇒ h = 380/(10×8) = 4.75 m
Hence, the height of cuboidal vessel be 4.75 m.
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm³ of wood has a mass of 0.6 g.
Inner radius of cylindrical pipe r = 24/2 = 12 cm, outer radius R = 28/2 = 14 cm and lenght h = 35 m Volume of cylindrical wooden pipe = π(R² - r²)h = 22/7 × (14² - 12²) × 35 = 22 × (196 - 144 ) × 5 = 22 × 52 × 5 = 5720 cm³ Mass of cylindrical wooden pipe = 5720 × 0.6 g = 3432 g = 3.432 kg [∵ 1 cm³Read more
Inner radius of cylindrical pipe r = 24/2 = 12 cm, outer radius R = 28/2 = 14 cm and lenght h = 35 m
See lessVolume of cylindrical wooden pipe = π(R² – r²)h
= 22/7 × (14² – 12²) × 35 = 22 × (196 – 144 ) × 5 = 22 × 52 × 5 = 5720 cm³
Mass of cylindrical wooden pipe = 5720 × 0.6 g = 3432 g = 3.432 kg [∵ 1 cm³ of wood has a mass of 0.6 g]
Hence, the volume of cylindrical wooden pipe is 3.432 kg.
A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
Length of tin can l = 5 cm, breadth b = 4 cm and height h = 15 cm Volume of tin can = lbh = 5 × 4 × 15 = 300 cm³ Radius of plastic cylinder r = 7/2 = 3.5 cm and height H = 10 cm Volume of plastic cylinder = πr²H 22/7 × 3.5 × 3.5 × 10 = 22 × 0.5 × 3.5 × 10 = 385 cm³ Difference between capacities of tRead more
Length of tin can l = 5 cm, breadth b = 4 cm and height h = 15 cm
See lessVolume of tin can = lbh = 5 × 4 × 15 = 300 cm³
Radius of plastic cylinder r = 7/2 = 3.5 cm and height H = 10 cm
Volume of plastic cylinder = πr²H
22/7 × 3.5 × 3.5 × 10 = 22 × 0.5 × 3.5 × 10 = 385 cm³
Difference between capacities of two packs = 385 – 300 = 85 cm³
Hence, the capacity of plastic cylindrical pack is greater than tin can by 85 cm³.
If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find (i) radius of its base. (ii) its volume. (Use π= 3.14)
(I) Lateral surface area of cylinder C = 94.2 cm² and height h = 5 cm. Let, the radius of cylinder = r cm Lateral surface area of cylinder C = 2πrh ⇒ 94.2 = 2 × 3.14 × r × 5 ⇒ r = (94.2)/(3.14×10) = 3 cm Hence, the radius of base is 3 cm. (II) Volume of cylinder = πr²h = 3.14 × 3 × 3 × 5 = 141.3 cm³Read more
(I) Lateral surface area of cylinder C = 94.2 cm² and height h = 5 cm.
Let, the radius of cylinder = r cm
Lateral surface area of cylinder C = 2πrh
⇒ 94.2 = 2 × 3.14 × r × 5 ⇒ r = (94.2)/(3.14×10) = 3 cm
Hence, the radius of base is 3 cm.
(II) Volume of cylinder = πr²h = 3.14 × 3 × 3 × 5 = 141.3 cm³
Hence, the volume of cylinder is 141.3 cm³.
See lessIt costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m², find
(I) Cost of painting the inner curved surface of cylindrical vessel = Rs 2200 and height h = 10 m. Let, the inner radius of cylindrical vessel = r m The inner curved surface area of cylindrical vessel = 2πrh The cost of painting is at the rate of Rs 20 per m² = Rs 20 × 2πrh According to question, RsRead more
(I) Cost of painting the inner curved surface of cylindrical vessel = Rs 2200 and height h = 10 m.
Let, the inner radius of cylindrical vessel = r m
The inner curved surface area of cylindrical vessel = 2πrh
The cost of painting is at the rate of Rs 20 per m² = Rs 20 × 2πrh
According to question, Rs 20 × 2πrh = 2200
⇒ 2πrh = 2200/20 = 110
Hence, the inner curved surface area is 110 m².
(II) The inner curved surface area of cylindrical vessel = 2πrh
⇒ 110 = 2 × 22/7 × r × 10 ⇒ r = 110×7/22×2×10 = 7/4 = 1.75 m
Hence, the radius of base of cylindrical vessel is 1.75 m.
(III) Volume of cylindrical cessel = πr²h
See less= 22/7 × 1.75 × 1.75 × 10 = 22 × 0.25 × 1.75 × 10 = 96.25 m³
Hence, the volume of cylindrical vessel is 96.25 m³.
The capacity of a closed cylindrical vessel of height 1 m is 15.4 liters. How many square meters of metal sheet would be needed to make it?
Capacity of cylindrical vessel V = 15.4 litres = 15.4/1000m³ = 0.0154 m³ and height h = 1 m Let, the radius of cylindrical vessel = r m Volume of cylindrical vessel V = πr²h ⇒ 0.0154 = 22/7 r²× 1 ⇒ r² = 0.0154 × 7/22 = 0.0049 ⇒ r = √0.0049 = 0.07 m Total surface area of cylindrical vessel = 2πr(r +hRead more
Capacity of cylindrical vessel V = 15.4 litres = 15.4/1000m³ = 0.0154 m³ and height h = 1 m
See lessLet, the radius of cylindrical vessel = r m
Volume of cylindrical vessel V = πr²h
⇒ 0.0154 = 22/7 r²× 1
⇒ r² = 0.0154 × 7/22 = 0.0049
⇒ r = √0.0049 = 0.07 m
Total surface area of cylindrical vessel = 2πr(r +h)
= 2 × 22/7 × 0.07 × (0.07 + 1) = 2 × 22 × 0.01 × 1.07 = 0.4708 m²
Hence, 0.4708 m² metal sheet is required to make this cylindrical vessel.
Find the surface area of a sphere of radius: 10.5 cm
Radis of sphere r = 10.5 cm Surface area of sphere = 4πr² = 4 × 22/7 × 10.5 × 10.5 = 4 × 22 × 1.5 × 10.5 = 1386.00 cm² Hence, the surface area of sphere is 1386 cm²
Radis of sphere r = 10.5 cm
See lessSurface area of sphere = 4πr²
= 4 × 22/7 × 10.5 × 10.5 = 4 × 22 × 1.5 × 10.5 = 1386.00 cm²
Hence, the surface area of sphere is 1386 cm²
A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
Speed of river l = 2 Km/h = 2000 m/h, breadth b = 40 m and height h = 15 m Volume of water fall into the sea in 1 hour = lbh = 2000 × 40 × 3 = 240000 m³ So, volume of water fall into the sea in 1 minute = 240000m³/60 = 4000 m³ Hence, in 1 minute, 4000 m³ will fall into the sea.
Speed of river l = 2 Km/h = 2000 m/h, breadth b = 40 m and height h = 15 m
See lessVolume of water fall into the sea in 1 hour = lbh = 2000 × 40 × 3 = 240000 m³
So, volume of water fall into the sea in 1 minute = 240000m³/60 = 4000 m³
Hence, in 1 minute, 4000 m³ will fall into the sea.
The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
First case: Radius of balloon r = 7 cm Surface area of balloon = 4πr² = 4 × 22/7 × 7 × 7 = 4 × 22 × 7 = 616 cm² Hence, the surface area of ballon is 616 cm² Second case: Radius of balloon R = 14 cm Surface area of bolloon = 4πR² = 4 × 22/7 × 14 × 14 = 4 × 22 × 2 × 14 = 2464 cm² Hence, the surface arRead more
First case:
See lessRadius of balloon r = 7 cm
Surface area of balloon = 4πr²
= 4 × 22/7 × 7 × 7 = 4 × 22 × 7 = 616 cm²
Hence, the surface area of ballon is 616 cm²
Second case:
Radius of balloon R = 14 cm
Surface area of bolloon = 4πR²
= 4 × 22/7 × 14 × 14
= 4 × 22 × 2 × 14
= 2464 cm²
Hence, the surface area of balloon is 2464 cm².
Ratio of surface area = 616/2464 = 1/4
Hence, the ratio of surface areas in two cases is 1:4
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many liters of water can it hold? (1m³ = 1000 l)
Length of water tank l = 6 m, breadth b = 5 m and height h = 4.5 m Volume of water tank = lbh = 6 × 5 × 4.5 = 135 cm³ = 135 × 1000 l = 135000 l Hence, the water tank can hold 135000 litres of water.
Length of water tank l = 6 m, breadth b = 5 m and height h = 4.5 m
See lessVolume of water tank = lbh = 6 × 5 × 4.5 = 135 cm³ = 135 × 1000 l = 135000 l
Hence, the water tank can hold 135000 litres of water.
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic meters of a liquid?
Length of cuboidal vessel l = 10 m, breadth b = 8 m and volume V = 380 m³ Let, the heigth of cuboidal vessel = h m Volume of cuboidal vessel = lbh ⇒ 380 = 10 × 8 × h ⇒ h = 380/(10×8) = 4.75 m Hence, the height of cuboidal vessel be 4.75 m.
Length of cuboidal vessel l = 10 m, breadth b = 8 m and volume V = 380 m³
See lessLet, the heigth of cuboidal vessel = h m
Volume of cuboidal vessel = lbh
⇒ 380 = 10 × 8 × h
⇒ h = 380/(10×8) = 4.75 m
Hence, the height of cuboidal vessel be 4.75 m.