Predict the change in surface area and volume of a spherical cell if the diameter of the cell doubles:

Question

Quizplus · Accepted Answer

The formula for the surface area of a sphere is 4πr^2, where r is the radius of the sphere. When the diameter of the sphere doubles, its radius will also double. So, the new surface area will be:

4π(2r)^2 = 4π(4r^2) = 16πr^2

This is four times the original surface area, so the surface area will increase by a factor of 4.

The formula for the volume of a sphere is (4/3)πr^3. When the diameter of the sphere doubles, its radius will also double. So, the new volume will be:

(4/3)π(2r)^3 = (4/3)π(8r^3) = (32/3)πr^3

This is eight times the original volume, so the volume will increase by a factor of 8.

Therefore, the correct answer is A.

Predict the Change in Surface Area and Volume of a Spherical