Question

The radii of circular ends of a bucket of height 24 cm are 15 cm and 5 cm. Find the area of its curved surface.

Answer 1

Answer

Curved surface area of bucket is 1632.8 sq cm

Solution

The radii of circular ends of a bucket of height 24 cm are 15 cm and 5 cm.

The bucket is like a frustum, with two radius R=15cm and r= 5cm.Height = 24cm. To find the curved surface area of bucket is the curved surface area of frustum.

Curved surface area, A= π(R + r)×$\sqrt{(R-r)^{2}+h^{2}}$

Here, R=15cm, r=5cm and h=24cm

Substituting in equation of area,

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

           A=3.14 x 20 x 26=1632.8 sq cm

Curved surface area of Bucket =1632.8 sq cm

Answer 2

Given,
height of bucket , h = 24cm
radius of circular ends of bucket are 5cm and 15cm
Let, $r_1=5cm,r_2=15cm$
then, slant height of bucket is given by ,
$l=\sqrt{h^2+(r_2-r_1)^2}$
$l=\sqrt{24^2+(15-5)^2}=\sqrt{676}=26cm$

now, curved surface area of bucket is given by,
$A=\pi(r_1+r_2)l$

or, A = π(15 + 5) × 26

or, A = π × 20 × 26

or, A = 520π cm²

hence, curved surface area of bucket is 520π cm²