Question

The rate of change of volume of a sphere with respect to its surface area when the radius is 4 cm is:

• A. (A) 4 cm3/cm2
• B. (B) 6 cm3/cm2
• C. (C) 2 cm3/cm2
• D. (D) 8 cm3/cm2

Answer 1

Answer: (C)

(C) 2 cm3/cm2

Answer 2

Explanation:

We know that, volume of sphere V=43πr3Surface area of sphere S=4πr2, where r is the radius of the sphere.So, rate of change of volume of sphere,⇒dVdt=ddt(43πr3)=43×3×πr2drdt⇒dVdt=4πr2drdt ----(1)Rate of change of surface area of sphere,⇒dSdt=ddt(4πr2)=4π×2×rdrdt⇒dSdt=8πrdrdt ----(2)From equation (1) and equation (2),⇒dVdS=dVdtdSdt=4πr2drdt8πrdrdt⇒4r8=2(∵r=4 cm)Therefore, the rate of change of volume of a sphere with respect to its surface area is 2 cm3/cm2.Hence, the correct option is (C).