Question : The area of the base of a solid cone is 616 cm2. If the height of the cone is 15 cm, then what is the volume of this cone?
Option 1: 2940 cm3
Option 2: 3440 cm3
Option 3: 3190 cm3
Option 4: 3080 cm3
Correct Answer: 3080 cm 3
Solution :
Area of the base of the Cone($A$)
⇒ $A$ = πr
2
= 616 cm
2
and $h$ = 15 cm
⇒ r
2
= $\frac{616}{π}$
The formula for the volume ($V$) of a cone is given by:
V = $\frac{1}{3}$πr
2
h, where:
$r$ is the radius of the base
$h$ is the height
⇒ Volume = $\frac{1}{3}$π $(\sqrt\frac{616}{π})^{2}$ × 15 = $\frac{1}{3}$π$\frac{616}{π}$ × 15 = $\frac{1}{3}$ × 616 × 15 = 3080 cm
3
Hence, the correct answer is 3080 cm
3
.
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