Question

A bucket is in the form of a frustum of a cone. The curved surface area of the bucket is $120\pi {cm}^2.$ The top and bottom radius of the bucket is $8cm$ and $4cm.$ What is the slant height ?

• A. $11cm$
• B. $10cm$
• C. $9cm$
• D. $13cm$

Answer 1

The correct option is B $10cm$

The curved surface area of a frustum of a cone is given by $\pi (R+r)l$ where $l$ is the slant height and $r,R$ is top and bottom radius.

So, by using the given information,

$\begin{array}{cc}\pi \left(R+r\right)l& =120\pi \\ \left(8+4\right)l& =120\\ 12l& =120\\ l& =10cm\end{array}$

Hence, the slant height of the bucket is $10cm.$