In a cone, the radius is 8 cm and the lateral surface area is 136pi cm^2.
1. find the slant height of the cone.
2.Find the height of the cone.
3.Find the volume of the cone, in terms of pi.
+118723 In a cone, the radius is 8 cm and the lateral surface area is 136pi cm^2.
1. find the slant height of the cone.
2.Find the height of the cone.
3.Find the volume of the cone, in terms of pi.
The lateral surface area of a cone is given by the formula pi*r*L where L is the slant height.
\(Lateral\; Surface\; area=\pi rl\\ 136\pi = \pi \times 8 \times l\\ 136=8 \times l\\ 17=l\\ slant\;height=17\;cm \)
The radius is 8cm and the slant height is 17cm
so
\(h^2=17^2-8^2\\ h^2=289-64\\ h^2=225\\ h=15\; cm\)
A cone is a circular pyramid and the volume of any pyramid is V = (1/3) * area of base * perpendicular height
\(Area \;of \;base = \pi*r^2 = \pi * 8^2 = 64\pi\)
\(V=\frac{1}{3}*64\pi*15\\ V=64\pi*5\\ V=320\pi\;\;cm^3\\\)
+118723 In a cone, the radius is 8 cm and the lateral surface area is 136pi cm^2.
1. find the slant height of the cone.
2.Find the height of the cone.
3.Find the volume of the cone, in terms of pi.
The lateral surface area of a cone is given by the formula pi*r*L where L is the slant height.
\(Lateral\; Surface\; area=\pi rl\\ 136\pi = \pi \times 8 \times l\\ 136=8 \times l\\ 17=l\\ slant\;height=17\;cm \)
The radius is 8cm and the slant height is 17cm
so
\(h^2=17^2-8^2\\ h^2=289-64\\ h^2=225\\ h=15\; cm\)
A cone is a circular pyramid and the volume of any pyramid is V = (1/3) * area of base * perpendicular height
\(Area \;of \;base = \pi*r^2 = \pi * 8^2 = 64\pi\)
\(V=\frac{1}{3}*64\pi*15\\ V=64\pi*5\\ V=320\pi\;\;cm^3\\\)
