Question

The radius of a sphere increases from 3 units to 5 units. What is the increase in the following quantities?

• A. $64\pi uni{t}^2$
• B. $\frac{392}{3}\pi$
• C. $2unit$

Answer 1

Initial radius $\left(r\right)=3$ unit
Final radius $\left(R\right)=5$ unit
Increase in radius $=5-3=2$ unit

Initial Surface Area $=4\pi r^2=4\pi (3{)}^2=36\pi uni{t}^2$

Final Surface Area $=4\pi R^2=4\pi (5{)}^2=100\pi uni{t}^2$

Increase in Surface Area $=100\pi -36\pi$
Increase in Surface Area $=64\pi uni{t}^2$

Initial Volume $=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (3{)}^3=\frac{108}{3}\pi uni{t}^3$

Final Volume $=\frac{4}{3}\pi R^3=\frac{4}{3}\pi (5{)}^3=\frac{500}{3}\pi uni{t}^3$

Increase in Volume $=\frac{500-108}{3}\pi$

Increase in Volume $=\frac{392}{3}\pi uni{t}^3$