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Surface Areas and Volumes

Short Answer Type

351. Three solid spheres of iron whose diameters are 2 cm, 12 cm and 16 cm respectively are melted into a single solid sphere. Find the radius of the solid sphere.

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352. A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.

V₁ = Volume of the cone

equals space space 1 third πr squared straight h equals space space 1 third πr squared equals space space 1 third πr cubed

V1 = Volume of the coneV2 = Volume of the hemisphere V3 = Volume

V₂ = Volume of the hemisphere

equals 2 over 3 πr cubed

V₃ = Volume of the cylinder = πr²h = πr²r = πr³r

therefore space space space straight V subscript 1 space colon space straight V subscript 2 space colon space straight V subscript 3 space equals 1 third πr cubed space colon 2 over 3 πr cubed colon πr cubed

= 1 : 2 :3

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353. A spherical ball of lead 3 cm in radius is melted and recast into three spherical balls. If the radii of two balls are

3 over 2

cm and 2 cm, find the diameter of the third ball.

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354. The volumes of two spheres are in the ratio 64 : 27. Find the difference of their surface areas, if the sum of their radii is 7 cm.

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355. A hemispherical bowl of internal diameter 36 cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?

open square brackets Use space straight pi equals 22 over 7 close square brackets

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356. A hemispherical bowl is made of steel 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

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357.

A spherical iron shell with 8 cm external diameter weighs $1860 4 over 7 straight g.$
Find the sick ness of the shell if the density of metal is 12 g/cm³ .