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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.

Let the radius of the solid sphere be R cm.
Then, according to the question,

$4 over 5 πR cubed equals 4 over 3 straight pi open parentheses 2 over 2 close parentheses cubed plus 4 over 3 straight pi open parentheses 12 over 2 close parentheses cubed plus 4 over 3 straight pi open parentheses 16 over 2 close parentheses cubed rightwards double arrow space space space straight R cubed equals 1 plus 216 plus 512 rightwards double arrow space space space straight R cubed equals 729 equals 9 cubed rightwards double arrow space space space straight R space equals space 9 space cm$

Hence, the radius of the solid sphere is 9 cm.

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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.

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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 .