- 3 cm
- 4 cm
- 5 cm
- 6 cm

Option 4 : 6 cm

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10 Questions
10 Marks
7 Mins

**GIVEN:**

Radius of sphere = 3 cm

Height of the cone = Half of the radius of the cone

**CONCEPT:**

Volume of Sphere = Volume of Cone

**FORMULA USED:**

Volume of Sphere = 4/3 × πR^{3}

Volume of Cone = 1/3 × πr^{2}h

**CALCULATION:**

Suppose the height and radius of the cone are ‘h’ and ‘r’ respectively.

∴ h = r/2

Now,

Applying the formula:

\(\frac{4}{3} \times \pi \times 3 \times 3 \times 3 = \frac{1}{3} \times \pi \times r \times r \times h\)

Put h = r/2

⇒ \(\frac{4}{3} \times 3 \times 3 \times 3 = \frac{1}{3} \times r \times r \times \frac{r}{2}\)

⇒ r^{3} = 216

⇒ r = 6

**∴ Radius of the cone = 6 cm.**

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