Question

A bucket is in a shape of a frustum, $40cm$ in diameter at the top and $28cm$ in diameter at the bottom. Find the cost of the tin sheet used in making the bucket, if the cost of tin is $Rs.1.50$ per sq dm.

• A. $Rs.44.25$
• B. $Rs.42.25$
• C. $Rs.40.25$
• D. $Rs.45.25$

Answer 1

The correct option is A $Rs.44.25$

Given:-

$r_1=20cm,r_2=14cm$ and $h=21cm$

If $l$ is the slant height of the bucket then,

$\begin{array}{cc}l& =\sqrt{{(r_1-r_2)}^2+h^2}\\ & =\sqrt{{(20-14)}^2+{21}^2}\\ & =\sqrt{6^2+{21}^2}\\ & =\sqrt{36+441}\\ & =\sqrt{477}\\ & =21.84cm\end{array}$

Total surface area of the bucket (which is open at the top)

$A=\pi l(r_1+r_2)+\pi r_2^2$

$=\pi \left[\right(r_1+r_2)l+r_2^2]$

$=\frac{22}{7}\left[\right(20+14)21.84+{14}^2]$

$=2949.76c{m}^2$

$1d{m}^2=100c{m}^2$

$A=\frac{2949.7}{100}$

$=29.497d{m}^2$

Required cost of the tin sheet at the rate of $Rs.1.50$ per sq. dm is

$\text{Cost}=1.50\times 2949.76$

$=Rs.44.25$