Answer to Question #150225 in Geometry for solid mensuration

Question

8. A right circular cylinder with an altitude of 40 cm and base diameter of 30cm has a right circular cone at its top with the same base. If the cone is 60cm high, determine its lateral area in cm2.

a) 706.86
b) 2,827.43
c) 2,914.45
d) 3,345.76

Answer 1

The lateral area of a right circular cone with a slant height $l$ and base radius $r$ can be found by the formula

$$A_L=\pi rl$$

By the Pythagorean Theorem from the right triangle

$$l^2=r^2+h^2,$$

where $h$ is an altitude of a cone.

Given $d=30\ cm, h=60\ cm.$

Then

$$r=\dfrac{d}{2}=\dfrac{30\ cm}{2}=15\ cm$$

$$l=\sqrt{r^2+h^2}=\sqrt{(15\ cm)^2+(60\ cm)^2}=15\sqrt{17}\ cm$$

$$A_L=\pi(15\ cm)(15\sqrt{17}\ cm)=(225\sqrt{17})\pi\ cm^2$$

$$\approx2914.45\ cm^2$$

c) 2,914.45