Question

the radius of sphere is increased by 30% by what percent does its volume increase​

Answer 1

QUESTIONS

the radius of sphere is increased by 30% by what percent does its volume increase

ANSWER

REFER to the attachment

Answer 2

Question:

The radius of sphere is increased by 30% by what percent does its volume increase.

Solution:

Volume of sphere $= \frac{4}{3} {\pi r}^{3}$

Area of sphere $= {4 \pi r}^{2}$

New Area $= {4 \pi R}^{2} = 1.30 \times {4 \pi r}^{2}$

→ R = √1.30r

New Volume $= \frac{4}{3} \pi {R}^{2}$

→ $\frac{4}{3} \pi ({1.30r}^{2} \times \sqrt{1.30}r$

→ $4 \times 1.30 \times \sqrt{1.30} \pi \frac{{r}^{3}}{3}$

Change in volume $= \frac{4}{3} \pi ({1.30r}^{2} \times \sqrt{1.30} - 1)$

As percentage,

→ (1.30 × √1.30 - 1) × 100

→ ${130}^{\frac{3}{2}} \times 100$