Question : A hemisphere of lead of radius 4 cm is cast into a right circular cone of height 72 cm. What is the radius of the base of the cone?
Option 1: 1.63 cm
Option 2: 1.35 cm
Option 3: 1.33 cm
Option 4: 1.45 cm
Correct Answer: 1.33 cm
Solution :
Volume of hemisphere = $\frac{ 2 \pi \times \text{Radius}^3}{3}$
Volume of cone = $\frac{\pi \times \text{Radius}^2 \times \text{Height}}{3}$
Given, Radius = 4 cm
Volume of hemisphere = $\frac{ 2 \pi \times 4^3}{3}$ = $\frac{ 128 \pi}{3}$ cm
3
Height of the cone = 72 cm
Let the radius of the base of the right circular cone be $R$ cm.
Volume of the cone = $\frac{\pi \times R^2 \times 72}{3}$
According to the question,
$\frac{ 128 \pi}{3} = \frac{\pi \times R^2 \times 72}{3}$
$⇒R^2 = \frac{16}{9}$
$⇒R = \frac{4}{3}$
$\therefore R= 1.33$
$\therefore$ The radius of the base of the cone is 1.33 cm.
Hence, the correct answer is 1.33 cm.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Get Updates BrochureYour Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.