Question

A right pyramid has a surface area of 258 cm2.
A right cone has a base radius of 4 cm. The
cone and pyramid have equal surface areas.
What is the height of the cone to the nearest
tenth of a centimetre?

Answer 1

surface arena of a cone:

A=pi*r(r+sqrt(h^2+r^2))
where r=radius

Given:
A= 258 cm^2
r=4 cm

find h

258=(3.14*4)(4+sqrt(h^2+4^2))

258=12.56(4+sqrt(h^2+16))

258/12.56 = 4+sqrt(h^2+16)

16.54 = sqrt(h^2+16)

square both sides

274.233 = h^2 + 16

258.233 = h^2

h=16.0696