Question

If the radius of a sphere increases from 4 centimeters to 7 centimeters, what will the difference between the volumes of both the spheres be?

• A. $\frac{1327}{3}\pi$ cu cm
• B. $\frac{1071}{3}\pi$ cu cm
• C. $\frac{1116}{3}\pi$ cu cm
• D. $\frac{1583}{3}\pi$ cu cm

Answer 1

The correct option is C $\frac{1116}{3}\pi$ cu cm

The figure based on the given data can be drawn as follows:


The formula to calculate the volume of the sphere is $V=\frac{4}{3}\pi r^3.$

Let the original sphere be the sphere with radius 4 cm.

Volume of the original sphere $=\frac{4}{3}\pi (4{)}^3=\frac{256}{3}\pi$ cu cm

The radius of the new sphere is 7 cm.
Volume of the new sphere $=\frac{4}{3}\pi (7{)}^3=\frac{1372}{3}\pi$ cu cm

Difference between the volume of the new sphere and the original sphere = volume of the new sphere - volume of the original sphere $=\frac{1372}{3}\pi -\frac{256}{3}\pi =\frac{1116}{3}\pi$ cu cm