Inner radius of wood in pencil r = 1/2 = 0.5 mm = 0.05 cm, Outer radius R = 7/2 = 3.5 mm = 0.35 cm and length h = 14 cm Volume of wood used in pencil = π(R² - r²)h = 22/7 × [(0.35)² - (0.05)²] × 14 = 22 × (0.1225 - 0.0025) × 2 = 22 × 0.12 × 2 = 5.28 cm³ Radius of graphite inside the wood r = 1/2 = 0Read more
Inner radius of wood in pencil r = 1/2 = 0.5 mm = 0.05 cm,
Outer radius R = 7/2 = 3.5 mm = 0.35 cm and length h = 14 cm
Volume of wood used in pencil = π(R² – r²)h
= 22/7 × [(0.35)² – (0.05)²] × 14
= 22 × (0.1225 – 0.0025) × 2
= 22 × 0.12 × 2
= 5.28 cm³
Radius of graphite inside the wood r = 1/2 = 0.5 mm = 0.05 cm and height h = 14 cm.
Volume of graphite in pencil = πr²h
= 22/7 × (0.05)² × 14
= 22 × 0.0025 × 2
= 0.11 cm³
Hence, in pencil, the volume of wood is 5.28 cm³ and that of graphite is 0.11 cm³.
(I) Radius of cone r = 6 cm and height h = 7 cm Volume of cone = 1/3πr²h = 1/3 × 22/7 × 6 × 6 × 7 = 264 cm³ Hence, the volume of right circular cone is 264 cm³. (II) Radius of cone r = 3.5 cm and height h = 12 cm Volume of cone = 1/3πr²h = 1/3 × 22/7 × 3.5 × 3.5 × 12 = 154 cm³ Hence, the volume of rRead more
(I) Radius of cone r = 6 cm and height h = 7 cm
Volume of cone = 1/3πr²h
= 1/3 × 22/7 × 6 × 6 × 7 = 264 cm³
Hence, the volume of right circular cone is 264 cm³.
(II) Radius of cone r = 3.5 cm and height h = 12 cm
Volume of cone = 1/3πr²h
= 1/3 × 22/7 × 3.5 × 3.5 × 12 = 154 cm³
Hence, the volume of right circular cone is 154 cm³.
Radis of sphere r = 14 cm Surface area of sphere = 4πr² = 4 × 22/7 × 14 × 14 = 4 × 22 × 2 × 14 = 2464 cm² Hence, the surface area of sphere is 2464 cm².
Radis of sphere r = 14 cm
Surface area of sphere = 4πr²
= 4 × 22/7 × 14 × 14 = 4 × 22 × 2 × 14 = 2464 cm²
Hence, the surface area of sphere is 2464 cm².
Circumference of the base of a cylindrical vessel C = 132 cm height h = 25 cm Let, the radius of cylindrical vessel = r cm Circumference of base of cylindrical vessel = 2πr ⇒ 132 = 2πr ⇒ 132 = 2 × 22/7 × r ⇒ r = (132 × 7/22 × 2) ⇒ r = 21 cm Volume of cylindrical vessel = πr²h = 22/7 × 21 × 21 × 25 =Read more
Circumference of the base of a cylindrical vessel C = 132 cm height h = 25 cm
Let, the radius of cylindrical vessel = r cm
Circumference of base of cylindrical vessel = 2πr
⇒ 132 = 2πr ⇒ 132 = 2 × 22/7 × r
⇒ r = (132 × 7/22 × 2) ⇒ r = 21 cm
Volume of cylindrical vessel = πr²h
= 22/7 × 21 × 21 × 25
= 34650 cm³
= 34650/1000 = 34.65 litres [∵ 1000 cm³ = 1 litres]
Hence, the cylindrical vessel can hold 34.65 litres of water.
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.
Inner radius of wood in pencil r = 1/2 = 0.5 mm = 0.05 cm, Outer radius R = 7/2 = 3.5 mm = 0.35 cm and length h = 14 cm Volume of wood used in pencil = π(R² - r²)h = 22/7 × [(0.35)² - (0.05)²] × 14 = 22 × (0.1225 - 0.0025) × 2 = 22 × 0.12 × 2 = 5.28 cm³ Radius of graphite inside the wood r = 1/2 = 0Read more
Inner radius of wood in pencil r = 1/2 = 0.5 mm = 0.05 cm,
See lessOuter radius R = 7/2 = 3.5 mm = 0.35 cm and length h = 14 cm
Volume of wood used in pencil = π(R² – r²)h
= 22/7 × [(0.35)² – (0.05)²] × 14
= 22 × (0.1225 – 0.0025) × 2
= 22 × 0.12 × 2
= 5.28 cm³
Radius of graphite inside the wood r = 1/2 = 0.5 mm = 0.05 cm and height h = 14 cm.
Volume of graphite in pencil = πr²h
= 22/7 × (0.05)² × 14
= 22 × 0.0025 × 2
= 0.11 cm³
Hence, in pencil, the volume of wood is 5.28 cm³ and that of graphite is 0.11 cm³.
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?
Radius of cylindrical bowl r = 7/2 = 3.5 and height of soup inside the cylindrical bowl h = 4 cm Volume of cylindrical bowl = πr²h = 22/7 × (3.5)² × 4 = 22/7 × 3.5 × 3.5 × 4 = 22 × 0.5 × 3.5 × 4 = 154 cm³ Therefore, the volume of soup per day for 250 patient = 250 × 154 = 38500 cm³ Hence, hospital hRead more
Radius of cylindrical bowl r = 7/2 = 3.5 and height of soup inside the cylindrical bowl h = 4 cm
See lessVolume of cylindrical bowl = πr²h
= 22/7 × (3.5)² × 4
= 22/7 × 3.5 × 3.5 × 4
= 22 × 0.5 × 3.5 × 4
= 154 cm³
Therefore, the volume of soup per day for 250 patient = 250 × 154 = 38500 cm³
Hence, hospital has to prepare 38500 cm³ soup daily to serve 250 patients.
Find the volume of the right circular cone with
(I) Radius of cone r = 6 cm and height h = 7 cm Volume of cone = 1/3πr²h = 1/3 × 22/7 × 6 × 6 × 7 = 264 cm³ Hence, the volume of right circular cone is 264 cm³. (II) Radius of cone r = 3.5 cm and height h = 12 cm Volume of cone = 1/3πr²h = 1/3 × 22/7 × 3.5 × 3.5 × 12 = 154 cm³ Hence, the volume of rRead more
(I) Radius of cone r = 6 cm and height h = 7 cm
See lessVolume of cone = 1/3πr²h
= 1/3 × 22/7 × 6 × 6 × 7 = 264 cm³
Hence, the volume of right circular cone is 264 cm³.
(II) Radius of cone r = 3.5 cm and height h = 12 cm
Volume of cone = 1/3πr²h
= 1/3 × 22/7 × 3.5 × 3.5 × 12 = 154 cm³
Hence, the volume of right circular cone is 154 cm³.
Find the surface area of a sphere of radius: 14 cm.
Radis of sphere r = 14 cm Surface area of sphere = 4πr² = 4 × 22/7 × 14 × 14 = 4 × 22 × 2 × 14 = 2464 cm² Hence, the surface area of sphere is 2464 cm².
Radis of sphere r = 14 cm
See lessSurface area of sphere = 4πr²
= 4 × 22/7 × 14 × 14 = 4 × 22 × 2 × 14 = 2464 cm²
Hence, the surface area of sphere is 2464 cm².
The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm³= 1l)
Circumference of the base of a cylindrical vessel C = 132 cm height h = 25 cm Let, the radius of cylindrical vessel = r cm Circumference of base of cylindrical vessel = 2πr ⇒ 132 = 2πr ⇒ 132 = 2 × 22/7 × r ⇒ r = (132 × 7/22 × 2) ⇒ r = 21 cm Volume of cylindrical vessel = πr²h = 22/7 × 21 × 21 × 25 =Read more
Circumference of the base of a cylindrical vessel C = 132 cm height h = 25 cm
See lessLet, the radius of cylindrical vessel = r cm
Circumference of base of cylindrical vessel = 2πr
⇒ 132 = 2πr ⇒ 132 = 2 × 22/7 × r
⇒ r = (132 × 7/22 × 2) ⇒ r = 21 cm
Volume of cylindrical vessel = πr²h
= 22/7 × 21 × 21 × 25
= 34650 cm³
= 34650/1000 = 34.65 litres [∵ 1000 cm³ = 1 litres]
Hence, the cylindrical vessel can hold 34.65 litres of water.