Question

A bucket is of the shape of a frustum. If the radii of the circular ends are $28$ cm and $7$ cm and the height is $45$ cm. The capacity of the bucket is __________.

• A. $48150{\text{cm}}^3$
• B. $48510{\text{cm}}^3$
• C. $48105{\text{cm}}^3$
• D. $48205{\text{cm}}^3$

Answer 1

Answer: (B)

$48510{\text{cm}}^3$

Given that,

The bucket is in the shape of a frustum.

Height of the bucket $=45$ cm

Radius of the bigger circular end, $r_1=28$ cm

and, radius of the smaller circular end, $r_2=7$ cm

Volume of bucket $=\frac{\pi }{3}(r_1^2+r_1{r}_2+r_2^2)h$

$=\frac{22}{3\times 7}[{28}^2+28\times 7+7^2]\times 45c{m}^3$

$=\frac{22}{21}[784+196+49]\times 45c{m}^3$

$=\frac{22}{21}\times 1029\times 45c{m}^3$

$=48510c{m}^3$

Hence, the volume is $48510c{m}^3$