Answer to Question #281098 in Geometry for trish

Question

Find the lateral area and volume of the frustum of a right circular cone having a slant height of 14m and the radii of the bases are 4m and 1.5 m respectively.

Answer 1

The lateral area of the frustum of a right circular cone is equal to one-half of the sum of the circumferences of the bases multiplied by slant height

$$Lateral \ area=\dfrac{1}{2}(2\pi R+2\pi r)l$$

$$=\pi(R+r)l=\pi(4+1.5)(14)(m^2)=77\pi\ m^2$$

The frustum volume is

$$V=\dfrac{1}{3}\pi h(R^2+r^2+Rr)$$

$$h=\sqrt{l^2-(r-r)^2}=\sqrt{14^2-(4-1.5)^2}(m)$$

$$=\dfrac{\sqrt{759}}{2}(m)$$

$$V=\dfrac{1}{3}\pi (\dfrac{\sqrt{759}}{2})(4^2+1.5^2+4(1.5))(m^3)$$

$$=\dfrac{97\sqrt{759}}{24}\pi (m^3)$$