NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 12: Surface Areas & Volumes - Exercise 12.1

Question 20

Step 1: Recall formulas in SI units

• Volume of a sphere: \(V = \tfrac{4}{3} \pi r^3\) (in cubic metres, \(m^3\))
• Surface area of a sphere: \(A = 4 \pi r^2\) (in square metres, \(m^2\))

Step 2: Use the volume ratio

Given ratio of volumes: \(64 : 27\).

Since volume is proportional to \(r^3\),

\(\dfrac{r_1}{r_2} = \sqrt[3]{\dfrac{64}{27}} = \dfrac{4}{3}.\)

So the radii are in the ratio \(4 : 3\).

Step 3: Find the ratio of surface areas

Surface area is proportional to \(r^2\).

So, \(\dfrac{A_1}{A_2} = \left(\dfrac{r_1}{r_2}\right)^2 = \left(\dfrac{4}{3}\right)^2 = \dfrac{16}{9}.\)

Final Answer: The ratio of surface areas is \(16:9\) (Option D).