Question

(i) Prove that the surface area of a sphere of diameter
d is π^2and the volume is 1/6πd^3.
(ii) The volumes and diameters of a cone and sphere
are equal. Prove that the height of the cone is
twice the diameter of the sphere.
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Answer 1

Answer:

. How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius 8 cm?

Solution:

Given,

A solid sphere of radius, R = 8 cm

With this sphere, we have to make spherical balls of radius r = 1 cm

Let’s assume that the number of balls made as n

Then, we know that

Volume of the sphere = 4/3 πr3

The volume of the solid sphere = sum of the volumes of n spherical balls.

n x 4/3 πr3 = 4/3 πR3

n x 4/3 π(1)3 = 4/3 π(8)3

n = 83 = 512

Therefore, 512 balls can be made of radius 1 cm each with a solid sphere of radius 8 cm.

Answer 2

Answer:

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