Question

The volume of a frustum cone is 1,600 $m{m}^3$, whose base and upper area of a circle is 16 and 100 $m{m}^2$. Find the height of the cone.

• A. 30.76 mm
• B. 11.25 mm
• C. 12.25 mm
• D. 13.25 mm

Answer 1

The correct option is A 30.76 mm

Volume of a frustum cone = $\frac{1}{3}(A_1+A_2+\sqrt{A_1{A}_2})h$
1,600 = $\frac{1}{3}(16+100+\sqrt{16\times 100})\times h$
1,600 = $\frac{1}{3}(116+\sqrt{1600})\times h$
1,600 = $\frac{1}{3}(116+40)\times h$
1,600 = $\frac{1}{3}\times 156\times h$
h = $(1,600\times 3)/156=30.76mm$