Question

The base and top diameter of a cone is 1.2 mm and 0.5 mm respectively. The height of the cone is 24 mm. What is the volume of frustum of a cone? (Use $\pi$ = 3).

• A. 154.14 mm${}^3$
• B. 144.14 mm${}^3$
• C. 134.14 mm${}^3$
• D. 124.14 mm${}^3$

Answer 1

The correct option is A 154.14 mm${}^3$

Volume of the frustum cone is $V=\frac{\pi h}{3}(R^2+Rr+r^2)$

D = 0.5 m, d = 0.1 m, h = 4 m

Diameter = radius/2

Radius = 2 $\times$ diameter

Therefore, R = 2.4 mm, r = 0.25 mm

$V=(3\times 24)/\left(3\right)[{2.4}^2+2.4\times 0.25+{0.25}^2]$

$=$ 24[5.76 + 0.6 + 0.0625]

$=$ 24[6.4225]

$=$ 154.14 mm${}^3$