Question:
Choose the correct answer of the following question:
If the height of a bucket in the shape of frustum of a cone is 16 cm and the diameters of its two circular ends are 40 cm and 16 cm, then its slant height is
(a) $20 \mathrm{~cm}$
(b) $12 \sqrt{5} \mathrm{~cm}$
(c) $8 \sqrt{13} \mathrm{~cm}$
(d) $16 \mathrm{~cm}$
Solution:
We have,
Height of the frustum, $h=16 \mathrm{~cm}$,
Radii of the circular ends, $R=\frac{40}{2}=20 \mathrm{~cm}$ and $r=\frac{16}{2}=8 \mathrm{~cm}$
Now,
The slant height of the frustum, $l=\sqrt{(R-r)^{2}+h^{2}}$
$=\sqrt{(20-8)^{2}+16^{2}}$
$=\sqrt{12^{2}+16^{2}}$
$=\sqrt{144+256}$
$=\sqrt{400}$
$=20 \mathrm{~cm}$
Hence, the correct answer is option (a).