Question

A solid spherical item is melted into the shape of a cylinder mounted by a cone having same radius. The diameters of the cylinder and sphere are 21 cm each.What is the height (in cm) of the cone if the height of the cylinder is 7 cm? [Take ∏ = 22/7]

• A. 21
• B. 10.5
• C. 14
• D. 7

Answer 1

Answer:

A. 21

Diameter = 21 cm ⇒ Radius (r = 10.5) cm

Volume is conserved:

Volume of sphere = Volume of cylinder + Volume of cone

$\frac{4}{3}\pi r^3 = \pi r^2 h_{\text{cyl}} + \frac{1}{3}\pi r^2 h_{\text{cone}}$
Substitute values$((r = 10.5), (h_{\text{cyl}} = 7)):$

$\frac{4}{3}\pi r^3 = \pi r^2 \cdot 7 + \frac{1}{3}\pi r^2 h$

Divide both sides by (\pi r^2):

$\frac{4}{3}r = 7 + \frac{1}{3}h$

Substitute (r = 10.5):

$\frac{4}{3} \times 10.5 = 7 + \frac{1}{3}h$
$14 = 7 + \frac{1}{3}h$
$7 = \frac{1}{3}h$
h = 21
= 21 cm