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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.

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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.

Let the radius of the third ball be r cm. Then, according to the question,

4 over 3 straight pi left parenthesis 3 right parenthesis cubed equals 4 over 3 straight pi open parentheses 3 over 2 close parentheses cubed plus 4 over 3 straight pi left parenthesis 2 right parenthesis cubed plus 4 over 3 straight pi left parenthesis straight r right parenthesis cubed rightwards double arrow space space space 27 equals 27 over 8 plus 8 plus straight r cubed rightwards double arrow space space space straight r cubed equals 155 over 8 space rightwards double arrow space straight r equals fraction numerator square root of 155 over denominator 2 end fraction space cm rightwards double arrow space space space 2 straight r equals square root of 155 space cm

Hence, the diameter of the third ball is

square root of 155

cm.

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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 .

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358. Find the volume of a sphere of radius 11.2 cm.

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359. A shot-put is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.8 g per cm³, find the mass of the shot-put.

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360.

A hemispherical bowl has a radius of 3.5 cm. What would be the volume of water it would contain?

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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

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.