Question : If the area of the base of a cone is 154 cm2 and the area of its curved surface is 550 cm2, then its volume is:
Option 1: 1232 cm3
Option 2: 1122 cm3
Option 3: 1434 cm3
Option 4: 1535 cm3
Correct Answer: 1232 cm 3
Solution :
Given: Area of the base of a cone = 154 cm
2
Curved surface area of cone = 550 cm
2
We know that,
Area of the base of the cone with radius $r=\pi r^2$
⇒ $\pi r^2 = 154$
⇒ $\frac{22}{7}\times r^2 = 154$
⇒ $r=7$
Now, the curved surface area of the cone = $\pi r l$, where $l$ is the slant height.
⇒ $\pi r l = 550$
⇒ $\frac{22}{7}\times7\times l = 550$
⇒ $l=25$
Let the height of the cone be $h$.
By using the Pythagoras' theorem,
$l^2=h^2+r^2$
⇒ $25^2=h^2+7^2$
⇒ $625-49=h^2$
⇒ $h=24$
Now, volume of the cone = $\frac{1}{3}\pi r^2 h$
= $\frac{1}{3}\times\frac{22}{7}\times7\times7\times24$
= 1232 cm
3
Hence, the correct answer is 1232 cm
3
.
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