Question

15. A person has one ball of radius 5 cm.
With the same material, how many balls
of radius 2.5 cm can be made.
(a) 5
(b) 6
(c) 8
(d) 10
Solve it with expalanation​

Answer 1

Recall:

$\text {Volume of a sphere}= \dfrac{4}{3} \pi r^3$

Find the volume of the big ball:

$\text {Volume }= \dfrac{4}{3} \pi r^3$

$\text {Volume }= \dfrac{4}{3} \pi (5)^3$

$\text {Volume }= \dfrac{500\pi }{3} \text{ cm}^3$

Find the volume of a small ball:

$\text {Volume }= \dfrac{4}{3} \pi r^3$

$\text {Volume }= \dfrac{4}{3} \pi (2.5)^3$

$\text {Volume }= \dfrac{125\pi }{6} \text { cm}^3$

Find the number of small balls that can be made:

$\text {Number of balls } = \dfrac{500\pi }{3} \div \dfrac{125\pi }{6}$

$\text {Number of balls } = 8$

Answer: (c) 8

Answer 2

Answer:

The answer is c) 8

Step-by-step explanation:

No. of balls = volume of bigger ball / volume of smaller ball

= 4π(5)^3/4π(2.5)^3

= 5*5*5/2.5*2.5*2.5

= 2*2*2

= 8