Question : If the height and slant height of a cone are 21 cm and 29 cm, respectively. Find its volume. (Use $\pi=\frac{22}{7}$)
Option 1: 8800 cm3
Option 2: 8708 cm3
Option 3: 8440 cm3
Option 4: 8080 cm3
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Correct Answer: 8800 cm 3
Solution :
Given, height $= h = 21\ \mathrm{cm}$
Slant height $=l=29\ \mathrm{cm}$
Let $r$ be the radius.
We know, $l^2=h^2+r^2$
⇒ $r^2=l^2-h^2$
⇒ $r^2=29^2-21^2$
⇒ $r^2=841-441$
⇒ $r^2=400$
⇒ $r=20$ cm
Now, Volume $=\frac{1}{3}\pi r^2h$
$=\frac{1}{3}\times\frac{22}{7}\times(20)^2\times21$
$=\frac{1}{3}\times\frac{22}{7}\times400\times21$
$=8800$ cm
3
Hence, the correct answer is 8800 cm
3
.
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