Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

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.

583 Views

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.

148 Views

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.

250 Views

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.

1531 Views

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?

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

For bowl

Radius (R) =

36 over 2 equals 18 space cm

therefore

Volume =

4 over 3 πR cubed equals 4 over 3 straight pi left parenthesis 18 right parenthesis cubed space cm cubed

For bottle
r = 3 cm h = 6 cm
∴ Volume = $πr squared straight h$ = π (3)² (6) cm³ Let n bottles be required. Then,

$nπ left parenthesis 3 right parenthesis cubed left parenthesis 6 right parenthesis equals 4 over 3 straight pi left parenthesis 18 right parenthesis cubed rightwards double arrow space space space space space space straight n space equals space 144$

100 Views

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.

115 Views

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 .