Question:
Choose the correct answer of the following question:
The radii of the circular ends of a bucket of height 40 cm are 24 cm and 15 cm. The slant height (in cm) of the bucket is
(a) 41 (b) 43 (c) 49 (d) 51
Solution:
We have,
Height of the bucket, $h=40 \mathrm{~cm}$,
Radius of the upper end, $R=24 \mathrm{~cm}$ and
Radius of the lower end, $r=15 \mathrm{~cm}$
Now,
The slant height, $l=\sqrt{(R-r)^{2}+h^{2}}$
$=\sqrt{(24-15)^{2}+40^{2}}$
$=\sqrt{9^{2}+40^{2}}$
$=\sqrt{81+1600}$
$=\sqrt{1681}$
$=41 \mathrm{~cm}$
Hence, the correct answer is option (a).