Question

A right angle triangle of base 4 cm and height 3 cm is rotated about its height. The curved surface area and volume of the solid obtained are _____ ($inc{m}^2$) and _____ ($inc{m}^3$) respectively.

• A. $18\pi \&14\pi$
• B. $20\pi \&16\pi$
• C. $16\pi \&18\pi$
• D. $22\pi \&20\pi$

Answer 1

The correct option is B $20\pi \&16\pi$

As we rotate a right angle triangle about its height we get a cone.
Its radius = r = Base of the triangle = 4 cm
and, height = h= 3 cm

By Pythagoras' theorem;
$\text{Hypotenuse}=\sqrt{{\text{base}}^2+{\text{height}}^2}=\sqrt{4^2+3^2}=5cm$

Slant height of cone, $l=$ Hypotenuse = 5 cm

Curved surface area of the cone
$=\pi rl=\pi \times 4\times 5=20\pi c{m}^2$

Volume of the cone
$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \pi \times 16\times 3=16\pi c{m}^3$