Delhi Police Constable Exam Model Paper 10

Given:
Radius of sphere = x
Total surface area and volume of sphere is numerically equal.
Formula:
Total surface area of sphere = $4\mathit{\pi }{\mathit{r}}^2$
Volume of sphere = $\left(\frac{4}{3}\right)\mathit{\pi }{\mathit{r}}^3$
Calculation:
According to the question
$\left(\frac{4}{3}\right)\times \mathit{\pi }\times {\mathit{x}}^3=4\mathit{\pi }\times {\mathit{x}}^2$
⇒ $\left(\frac{1}{3}\right)\times {\mathit{x}}^3={\mathit{x}}^2$
⇒ x = 3 cm
∴ Radius of sphere is 3 cm.