If the radii of the circular ends of a bucket $ 24 \mathrm{~cm} $ high are $ 5 \mathrm{~cm} $ and $ 15 \mathrm{~cm} $ respectively, find the surface area of the bucket.


Given:

The radii of the circular ends of a bucket \( 24 \mathrm{~cm} \) high are \( 5 \mathrm{~cm} \) and \( 15 \mathrm{~cm} \) respectively.

To do:

We have to find the surface area of the bucket.

Solution:

Height of the bucket (frustum) $h = 24\ cm$

Radius of the top of the bucket $r_1 = 15\ cm$

Radius of the bottom of the bucket $r_2 = 5\ cm$

Therefore,

Lateral height of the bucket $l=\sqrt{(h)^{2}+(r_{1}-r_{2})^{2}}$

$=\sqrt{(24)^{2}+(15-5)^{2}}$

$=\sqrt{24^{2}+10^{2}}$

$=\sqrt{575+100}$

$=\sqrt{676}$

$=26$

Total surface area of the bucket $=\pi(r_{1}+r_{2}) l+\pi r_{2}^{2}$

$=\pi(15+5) \times 26+\pi \times(5)^{2}$

$=20 \times 26 \pi+25 \pi$

$=520 \pi+25 \pi$

$=545 \pi \mathrm{cm}^{2}$

The surface area of the bucket is $545 \pi \mathrm{cm}^{2}$.

Tutorialspoint
Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

32 Views

Kickstart Your Career

Get certified by completing the course

Get Started
Advertisements