Answer to Question #187581 in Geometry for John

Question

a large cone has a height 6 cm and base diameter 18 cm. The large cone is made by placing a small cone A of height 2 cm and base diameter 6 cm on top of a frustum B.

Calculate the volume of the frustum B. Give your answer in terms of π.​​​​​​​​

 

Calculate the total surface area of frustum B. Give your answer in terms of π.

Answer 1

$Volume \ of\ frustum\ of\ cone=\dfrac{{\pi}h(r_1^{2}+r_2^{2}+r_1r_2)}{3}$

$r_1=9\ cm$

$r_2=3\ cm$

$\ h=2\ cm$

$where\ r_1,r_2 \ radius$$\ of\ frustum\ and\ h_1\ height\ of frustum.$

Now putting all the value in above formula, we get

$V=\dfrac{{\pi}h(r_1^{2}+r_2^{2}+r_1+r_2)}{3}=\dfrac{{\pi}\times 2( 9^{2}+ 3^{2}+9\times3)}{3}=78{\pi}\ cm^{3}$

$Total\ surface \ area \ of frustum={\pi}({r_1^{2}}+{r_2^{2}}+(r_1+r_2)\times \sqrt({{r_1-r_2})^{2}+h^{2}})=$${\pi}\times(9^{2}+3^{2}+9+3 +\sqrt {(9-3)^{2}+2^{2}})$=216.64 ${\pi}$