Question

The height of a cone is 21 cm. Find the area of the base if the slant height is 28 cm.

Answer 1

The area of the base of a cone = 1078 $cm^{2}$

Step-by-step explanation:

Given,

The height of a cone (h) = 21 cm and

The slant height of a cone (l) = 28 cm

Let r be the radius of a cone.

To find, the area of the base of a cone = ?

We know that,

Slant height, l = $\sqrt{r^{2} +h^2}$

⇒ Radius, r = $\sqrt{l^{2} -h^2}$

= $\sqrt{28^{2} -21^2}$ = $\sqrt{784 -441}$

= $\sqrt{343}$ cm

= 7$\sqrt{7}$ cm

∴ The area of the base of a cone = $\pi r^2$

= $\dfrac{22}{7} (7\sqrt{7}) ^2 cm^2$

= $\dfrac{22}{7} (49\times 7)cm^2$

= 22 × 49 $cm^{2}$

= 1078 $cm^{2}$

Thus, the area of the base of a cone = 1078 $cm^{2}$