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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