Question

If the radius of spaher is increased by 100%the the volume of corresponding sphere increased by how much pecent

Answer 1

Volume of sphere before increasing its radius

= 4/3 πr³

After increasing the radius by 100% we get new radius:

radius, R = r + r×100/100

=> R = r + r

=> R = 2r

Volume = 4/3 × π(2r)³

=> 4/3 × π × 8r³

=> 32/3 × πr³

Percent Increased:

$</p><p></p><p>\rightarrow \quad \frac{\frac{32}{3} \pi r^{3}}{ \frac{4}{3} \pi r^{3} } \times 100</p><p></p><p>\\ \\</p><p></p><p>\rightarrow \quad \frac{\frac{32 \pi r^{3} }{3}}{ \frac{4 \pi r^{3}}{3} } \times 100</p><p></p><p>\\ \\</p><p></p><p>\rightarrow \quad \frac{32 \cancel{\pi r^{3}} }{\cancel{3}} \times \frac{\cancel{3}}{4 \cancel{\pi r^{3}} } \times 100</p><p></p><p>\\ \\</p><p></p><p>\rightarrow \frac{\cancel{32}}{\cancel{4}} \times 100</p><p></p><p>\\ \\</p><p></p><p>\rightarrow \quad 8 \times 100</p><p></p><p>\\ \\</p><p></p><p>\Rightarrow \quad 800</p><p></p><p>$

Therefore, The volume will increase by 800%