Length of cuboidal pit l = 8 m, breadth b = 6 m and height h = 3 m. Volume of cuboidal pit = lbh = 8 × 6 × 3 = 144 m³ Cost of digging at the rate of Rs 30 per m³ = Rs 144 × 30 = Rs 4320 Hence, the cost of digging the cuboidal pit is Rs 4320.
Length of cuboidal pit l = 8 m, breadth b = 6 m and height h = 3 m.
Volume of cuboidal pit = lbh = 8 × 6 × 3 = 144 m³
Cost of digging at the rate of Rs 30 per m³ = Rs 144 × 30 = Rs 4320
Hence, the cost of digging the cuboidal pit is Rs 4320.
Length of cuboidal tank l = 2.5 m, depth h = 10 m and volume V = 50000 litres = 50 m³ Let, the breadth of cuboidal tank = b m Volume of cuboidal tank = lbh ⇒ 50 = 2.5 × b × 10 ⇒ b = 50/2.5×10 = 2 m Hence, the breadth of cuboidal tank is 2 m.
Length of cuboidal tank l = 2.5 m, depth h = 10 m and volume V = 50000 litres = 50 m³
Let, the breadth of cuboidal tank = b m
Volume of cuboidal tank = lbh
⇒ 50 = 2.5 × b × 10
⇒ b = 50/2.5×10 = 2 m
Hence, the breadth of cuboidal tank is 2 m.
Length of tank l = 20 m, Breadth b = 15 m and height h = 6 m Volume of tank = lbh = 20 × 15 × 6 = 1800 m³ = 1800 × 1000 = 1800000 litres Daily requirement of water = 150 litres Therefore, the requirement of 4000 person for one day = 150 × 4000 = 600000 litres Hence, the number of days to consume allRead more
Length of tank l = 20 m, Breadth b = 15 m and height h = 6 m
Volume of tank = lbh = 20 × 15 × 6 = 1800 m³ = 1800 × 1000 = 1800000 litres
Daily requirement of water = 150 litres
Therefore, the requirement of 4000 person for one day = 150 × 4000 = 600000 litres
Hence, the number of days to consume all water of tank
Volume of tank/Volume of water for 4000 person for one day
= 1800000 litres/600000 litres = 3
Length of godown L = 40 m, breadth B = 25 m and height H = 15 m Volume of godown = LBH = 40 × 25 × 15 = 15000 m³ Length of crate l = 1.5 m, breadth b = 1.25 m and height h = 0.5 m Volume of crate = lbh = 1.5 × 1.25 × 0.5 = 0.9375 m³ Now, Number of crates to be stored in godown = Volume of godown/VolRead more
Length of godown L = 40 m, breadth B = 25 m and height H = 15 m
Volume of godown = LBH = 40 × 25 × 15 = 15000 m³
Length of crate l = 1.5 m, breadth b = 1.25 m and height h = 0.5 m
Volume of crate = lbh = 1.5 × 1.25 × 0.5 = 0.9375 m³
Now,
Number of crates to be stored in godown = Volume of godown/Volume of 1crate
= 15000 m³/0.9375 m³ = 10666.67
Hence, maximum of 10666 crates can be placed in the godown.
Side of larger cube A = 12 cm. Therefore, volume = A³ = 12 × 12 × 12 = 1728 cm³ According to question, Volume of smaller cube a³ = Volume of larger cube/8 = 1728 cm³/8 = 216 cm³ ⇒ a³ = 216 cm³ ⇒ a = √216 = 6 cm Hence, the side of new cube is cm. Now, ratio of surface areas of two cubes = Surface areRead more
Side of larger cube A = 12 cm. Therefore, volume = A³ = 12 × 12 × 12 = 1728 cm³
According to question, Volume of smaller cube
a³ = Volume of larger cube/8 = 1728 cm³/8 = 216 cm³
⇒ a³ = 216 cm³ ⇒ a = √216 = 6 cm
Hence, the side of new cube is cm.
Now,
ratio of surface areas of two cubes = Surface area of large cube/Surface area of smaller cube = 6A²/6a² = A²/a² = 12²/6² = 144/36 = 4:1
Radius of sphere r = 5.6 cm Surface area of sphere = 4πr² = 4 × 22/7 × 5.6 × 5.6 = 4 × 22 × 0.8 × 5.6 = 394.24 cm² Hence, the surface area of sphere is 394.24 cm².
Radius of sphere r = 5.6 cm
Surface area of sphere = 4πr²
= 4 × 22/7 × 5.6 × 5.6 = 4 × 22 × 0.8 × 5.6 = 394.24 cm²
Hence, the surface area of sphere is 394.24 cm².
Radius of sphere r = 21/2 = 10.5 cm Surface area of sphere = 4πr² = 4 × 22/7 × 10.5 × 10.5 = 4 × 22 × 4.5 × 10.5 = 1386 cm² Hence, the surface area of sphere is 1386 cm².
Radius of sphere r = 21/2 = 10.5 cm
Surface area of sphere = 4πr²
= 4 × 22/7 × 10.5 × 10.5 = 4 × 22 × 4.5 × 10.5 = 1386 cm²
Hence, the surface area of sphere is 1386 cm².
Radius of sphere r = 3.5/2 = 1.75 cm Surface area of sphere = 4πr² = 4 × 22/7 × 1.75 × 1.75 = 4 × 22 × 0.25 × 1.75 = 38.50 cm² Hence, the surface area of sphere is 38.5 cm².
Radius of sphere r = 3.5/2 = 1.75 cm
Surface area of sphere = 4πr²
= 4 × 22/7 × 1.75 × 1.75 = 4 × 22 × 0.25 × 1.75
= 38.50 cm²
Hence, the surface area of sphere is 38.5 cm².
Internal radius of hemispherical bowl r = 10.5/2 = 5.25 cm Inner surface area of hemispherical bowl = 2πr² = 2 × 22/7 × 5.25 × 5.25 = 2 × 22 × 0.75 × 5.25 = 173.25 cm² Cost of tin-plating the rate of Rs 16 per 100 cm² = Rs 173. 25 × 16/100 = Rs 27.72 Hence, the cost of tin- plating inside at the ratRead more
Internal radius of hemispherical bowl r = 10.5/2 = 5.25 cm
Inner surface area of hemispherical bowl = 2πr²
= 2 × 22/7 × 5.25 × 5.25
= 2 × 22 × 0.75 × 5.25
= 173.25 cm²
Cost of tin-plating the rate of Rs 16 per 100 cm²
= Rs 173. 25 × 16/100 = Rs 27.72
Hence, the cost of tin- plating inside at the rate of Rs 16 per 100 cm² is Rs 27.72.
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m³.
Length of cuboidal pit l = 8 m, breadth b = 6 m and height h = 3 m. Volume of cuboidal pit = lbh = 8 × 6 × 3 = 144 m³ Cost of digging at the rate of Rs 30 per m³ = Rs 144 × 30 = Rs 4320 Hence, the cost of digging the cuboidal pit is Rs 4320.
Length of cuboidal pit l = 8 m, breadth b = 6 m and height h = 3 m.
See lessVolume of cuboidal pit = lbh = 8 × 6 × 3 = 144 m³
Cost of digging at the rate of Rs 30 per m³ = Rs 144 × 30 = Rs 4320
Hence, the cost of digging the cuboidal pit is Rs 4320.
The capacity of a cuboidal tank is 50000 liters of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.
Length of cuboidal tank l = 2.5 m, depth h = 10 m and volume V = 50000 litres = 50 m³ Let, the breadth of cuboidal tank = b m Volume of cuboidal tank = lbh ⇒ 50 = 2.5 × b × 10 ⇒ b = 50/2.5×10 = 2 m Hence, the breadth of cuboidal tank is 2 m.
Length of cuboidal tank l = 2.5 m, depth h = 10 m and volume V = 50000 litres = 50 m³
See lessLet, the breadth of cuboidal tank = b m
Volume of cuboidal tank = lbh
⇒ 50 = 2.5 × b × 10
⇒ b = 50/2.5×10 = 2 m
Hence, the breadth of cuboidal tank is 2 m.
A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?
Length of tank l = 20 m, Breadth b = 15 m and height h = 6 m Volume of tank = lbh = 20 × 15 × 6 = 1800 m³ = 1800 × 1000 = 1800000 litres Daily requirement of water = 150 litres Therefore, the requirement of 4000 person for one day = 150 × 4000 = 600000 litres Hence, the number of days to consume allRead more
Length of tank l = 20 m, Breadth b = 15 m and height h = 6 m
See lessVolume of tank = lbh = 20 × 15 × 6 = 1800 m³ = 1800 × 1000 = 1800000 litres
Daily requirement of water = 150 litres
Therefore, the requirement of 4000 person for one day = 150 × 4000 = 600000 litres
Hence, the number of days to consume all water of tank
Volume of tank/Volume of water for 4000 person for one day
= 1800000 litres/600000 litres = 3
A godown measures 40 m × 25 m × 10 m. Find the maximum number of wooden crates each measuring 1.5 m × 1.25 m × 0.5 m that can be stored in the godown.
Length of godown L = 40 m, breadth B = 25 m and height H = 15 m Volume of godown = LBH = 40 × 25 × 15 = 15000 m³ Length of crate l = 1.5 m, breadth b = 1.25 m and height h = 0.5 m Volume of crate = lbh = 1.5 × 1.25 × 0.5 = 0.9375 m³ Now, Number of crates to be stored in godown = Volume of godown/VolRead more
Length of godown L = 40 m, breadth B = 25 m and height H = 15 m
See lessVolume of godown = LBH = 40 × 25 × 15 = 15000 m³
Length of crate l = 1.5 m, breadth b = 1.25 m and height h = 0.5 m
Volume of crate = lbh = 1.5 × 1.25 × 0.5 = 0.9375 m³
Now,
Number of crates to be stored in godown = Volume of godown/Volume of 1crate
= 15000 m³/0.9375 m³ = 10666.67
Hence, maximum of 10666 crates can be placed in the godown.
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.
Side of larger cube A = 12 cm. Therefore, volume = A³ = 12 × 12 × 12 = 1728 cm³ According to question, Volume of smaller cube a³ = Volume of larger cube/8 = 1728 cm³/8 = 216 cm³ ⇒ a³ = 216 cm³ ⇒ a = √216 = 6 cm Hence, the side of new cube is cm. Now, ratio of surface areas of two cubes = Surface areRead more
Side of larger cube A = 12 cm. Therefore, volume = A³ = 12 × 12 × 12 = 1728 cm³
See lessAccording to question, Volume of smaller cube
a³ = Volume of larger cube/8 = 1728 cm³/8 = 216 cm³
⇒ a³ = 216 cm³ ⇒ a = √216 = 6 cm
Hence, the side of new cube is cm.
Now,
ratio of surface areas of two cubes = Surface area of large cube/Surface area of smaller cube = 6A²/6a² = A²/a² = 12²/6² = 144/36 = 4:1
Find the surface area of a sphere of diameter: 14 cm.
Radius of sphere r = 14/2 = 7 cm Surface area of sphere = 4πr² = 4 × 22/7 × 7 × 7 = 4 × 22 × 7 = 616 cm² Hence, the surface area of sphere is 616 cm².
Radius of sphere r = 14/2 = 7 cm
See lessSurface area of sphere = 4πr²
= 4 × 22/7 × 7 × 7 = 4 × 22 × 7 = 616 cm²
Hence, the surface area of sphere is 616 cm².
Find the surface area of a sphere of radius: 5.6 cm
Radius of sphere r = 5.6 cm Surface area of sphere = 4πr² = 4 × 22/7 × 5.6 × 5.6 = 4 × 22 × 0.8 × 5.6 = 394.24 cm² Hence, the surface area of sphere is 394.24 cm².
Radius of sphere r = 5.6 cm
See lessSurface area of sphere = 4πr²
= 4 × 22/7 × 5.6 × 5.6 = 4 × 22 × 0.8 × 5.6 = 394.24 cm²
Hence, the surface area of sphere is 394.24 cm².
Find the surface area of a sphere of diameter: 21 cm.
Radius of sphere r = 21/2 = 10.5 cm Surface area of sphere = 4πr² = 4 × 22/7 × 10.5 × 10.5 = 4 × 22 × 4.5 × 10.5 = 1386 cm² Hence, the surface area of sphere is 1386 cm².
Radius of sphere r = 21/2 = 10.5 cm
See lessSurface area of sphere = 4πr²
= 4 × 22/7 × 10.5 × 10.5 = 4 × 22 × 4.5 × 10.5 = 1386 cm²
Hence, the surface area of sphere is 1386 cm².
Find the surface area of a sphere of diameter: 3.5 m.
Radius of sphere r = 3.5/2 = 1.75 cm Surface area of sphere = 4πr² = 4 × 22/7 × 1.75 × 1.75 = 4 × 22 × 0.25 × 1.75 = 38.50 cm² Hence, the surface area of sphere is 38.5 cm².
Radius of sphere r = 3.5/2 = 1.75 cm
See lessSurface area of sphere = 4πr²
= 4 × 22/7 × 1.75 × 1.75 = 4 × 22 × 0.25 × 1.75
= 38.50 cm²
Hence, the surface area of sphere is 38.5 cm².
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs 16 per 100 cm².
Internal radius of hemispherical bowl r = 10.5/2 = 5.25 cm Inner surface area of hemispherical bowl = 2πr² = 2 × 22/7 × 5.25 × 5.25 = 2 × 22 × 0.75 × 5.25 = 173.25 cm² Cost of tin-plating the rate of Rs 16 per 100 cm² = Rs 173. 25 × 16/100 = Rs 27.72 Hence, the cost of tin- plating inside at the ratRead more
Internal radius of hemispherical bowl r = 10.5/2 = 5.25 cm
See lessInner surface area of hemispherical bowl = 2πr²
= 2 × 22/7 × 5.25 × 5.25
= 2 × 22 × 0.75 × 5.25
= 173.25 cm²
Cost of tin-plating the rate of Rs 16 per 100 cm²
= Rs 173. 25 × 16/100 = Rs 27.72
Hence, the cost of tin- plating inside at the rate of Rs 16 per 100 cm² is Rs 27.72.