SSC MTS 2022 Question Paper Shift 1 (July 12th)

Question 74

The volume of a cone is 27720 $$cm^{3}$$. If the height of the cone is 20 cm, then what will be the area of the base?

Solution

The volume of a cone is 27720 $$cm^{3}$$.

volume of a cone = $$\frac{1}{3}\times\pi\times\left(radius\right)^2\ \times height$$

$$27720 = \frac{1}{3}\times\pi\times\left(radius\right)^2\ \times height$$

If the height of the cone is 20 cm.

$$27720=\frac{1}{3}\times\pi\times\left(radius\right)^2\ \times20$$

$$\frac{27720\times\ 3}{20}=\pi\times\left(radius\right)^2$$
$$1386\times\ 3=\pi\times\left(radius\right)^2$$
$$4158=\pi\times\left(radius\right)^2$$
Area of the base of a cone = $$\pi\times\left(radius\right)^2\ =\ 4158$$ $$cm^{2}$$

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