Problema Solution
A right pyramid has a surface area of 285cm. A right cone has a base radius of 4 cm. The cone and the pyramid have equal surface areas. What is the height of the cone to the nearest tenth of a centimetre
Answer provided by our tutors
surface area of a cone, 'A', is:
A=PI*r*s, where 'PI' is the numeric constant approximated by 3.14, 'r' is the radius and 's' is the slant height
total surface area for the cone is the surface area of the base (PI*r^2) plus the surface area of the side (PI*r*s)
285 = PI*4^2 + PI*4*s
s = (285-16*PI)/(4*PI)
the cone's slant height (285-16*PI)/(4*PI)), radius (4) and height, h' form the sides of a right triangle
we then have this right-triangle equation:
((285-16*PI)/(4*PI))^2 = 4^2 + h^2
solving for 'h' we have h=18.246
the height of the cone is approximately 18.2 cm