Question

A 15 cm tall cylindrical bucket of base diameter 6 cm, is recast to form a frustum with radii 2 cm and 4 cm. Find the height of the frustum obtained.

• A. 11.75 cm
• B. 14.47 cm
• C. 13.21 cm
• D. 12.52 cm

Answer 1

The correct option is B

14.47 cm

Given, height of cylindrical bucket, h = 15 cm
diameter of the cylindrical bucket = 6 cm
So, radius of bucket, r = $\frac{6}{2}$ = 3 cm.

Volume of the cylinder
$=\pi r^{2}h$
$=\pi \times (3{)}^2\times 15=135\pi c{m}^3$

Given, radii of frustum; r' = 2 cm and R = 4 cm.
Let h' be the height of the frustum.

Volume of the frustum
= $\frac{1}{3}\pi (R^2+(r^{\prime }{)}^2+R\times r^{\prime })h^{\prime }$
$=\frac{1}{3}\pi \times (4^2+2^2+4\times 2)\times h^{\prime }=9.33\pi h^{\prime }c{m}^3$

Given, cylindrical bucket is recast into a form of frustum. So, the shape changes but volume remains the same.
Volume of cylinder = Volume of frustum
135 $\pi$ = 9.33$\pi h^{\prime }$
$h^{\prime }=\frac{135}{9.33}cm$
$h^{\prime }=14.47cm$