Question

The volume of a frustum cone is 4,200 $c{m}^3$, whose base and upper area of a circle is 40 and 10 $c{m}^2$. Find the height of the cone.

• A. 140 cm
• B. 150 cm
• C. 180 cm
• D. 170 cm

Answer 1

The correct option is C 180 cm

Volume of a frustum cone = $\frac{1}{3}(A_1+A_2+\sqrt{A_1{A}_2})h$

4,200 = $\frac{1}{3}(40+10+\sqrt{40\times 10})\times h$

4,200 = $\frac{1}{3}(50+\sqrt{400})\times h$

4,200 = $\frac{1}{3}(50+20)\times h$

$4,200\times 3$ = $70\times h$

h = 4,200 $\times$ 3/70

h = 180 cm