Question : The volume of a right circular cone is 1232 cm3 and its vertical height is 24 cm. Its curved surface area is:
Option 1: 154 cm2
Option 2: 550 cm2
Option 3: 604 cm2
Option 4: 704 cm2
Correct Answer: 550 cm 2
Solution :
Given: The volume of a right circular cone is 1232 cm
3
and its vertical height is 24 cm.
Let $r$, $h$, and $l$ be the radius, height, and slant height of the cone.
According to the question,
$\frac{1}{3}×\pi×r^2×h=1232$
Or, $\frac{1}{3}×\frac{22}{7}×r^2×24=1232$
Or, $r^2=\frac{1232×7×3}{22×24}$
Or, $r^2=49$
Or, $r=7$ cm.
Now, $l^2=h^2+r^2$
Or, $l^2=24^2+7^2$
Or, $l^2=576+49$
Or, $l=\sqrt{625}=25$ cm.
Therefore, its curved surface area = $\pi×r×l$
= $\frac{22}{7}×7×25$
= 550 cm
2
.
Hence, the correct answer is 550 cm
2
.
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