Question

If the radius of a sphere is doubled, what will be the ratio of its surface area and volume as to that of the first sphere.

• A. $7:1,8:1$
• B. $5:1,8:1$
• C. $3:1,8:1$
• D. $4:1,8:1$

Answer 1

The correct option is D $4:1,8:1$

Let, the radius of the sphere be $r$ cm

Surface area of the original sphere $=4\pi r^2$

New radius of the sphere $2r$ cm

Surface area of the new sphere $=4\pi (2r{)}^2=4\pi \times 4r^2$

Therefore, required ratio $\frac{4\pi \times 4r^2}{4\pi r^2}$ $=4:1$

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

Volume of new sphere $=\frac{4}{3}\pi (2r{)}^3$

Required ratio $=\frac{\frac{4}{3}\pi (2r{)}^3}{\frac{4}{3}\pi r^3}$ $=8:1$