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Surface Areas and Volumes

Short Answer Type

331. A conical tent is to accommodate 11 persons. Each person must have 4 m² of the space on the ground and 20 m³ of air to breadth. Find the height and radius of the conical tent.

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332. A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m, find its volume.

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333. Find the volume of a right circular cone whose slant height is 13 cm and the diameter of the base is 10 cm. (Take

straight pi

= 3.14)

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334. Find the volume of a sphere whose radius is

7 cm

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335. Find the volume of a sphere whose radius is

0.63 m

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336. Find the amount of water displaced by a solid spherical ball of diameter
28 cm

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337. Find the amount of water displaced by a solid spherical ball of diameter
0.21 m.

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338. The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm³?

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339. The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

Let the radius of the earth be r.
Then, diameter of the earth = 2r

$therefore space$ Diameter of the moon $equals 1 fourth left parenthesis 2 straight r right parenthesis equals straight r over 2$

$therefore$ Radius of the moon = $1 half open parentheses r over 2 close parentheses equals r over 4$

Volume of the earth (v₁) = $4 over 3 πr cubed$
Volume of the moon (v₂)

$equals 4 over 3 straight pi open parentheses straight r over 4 close parentheses cubed equals 1 over 64 open parentheses 4 over 3 πr cubed close parentheses$

$equals 1 over 64$ (volume of the earth)

Hence, the volume of the moon is $1 over 64$ th fraction of the volume of the earth.

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340. How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

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