SOLUTION: Asking this question again as was responded too but no answer was given:
Need to find the surface area of composite figures and leave answer in terms of pi. The first figure is
Question 1044876: Asking this question again as was responded too but no answer was given:
Need to find the surface area of composite figures and leave answer in terms of pi. The first figure is a cone with a radius of 10mm and a height of 24mm (does not give the slant height) and inside is a hemisphere with a radius of 8mm.
The reason there was no answer is because of the words
"and inside is a hemisphere with a radius of 8mm."
Surface area problems are always about "outside" things
only, and never involve "inside" things.
Edwin
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website! In a right circular cone, the base radius, is perpendicular to the height, .
Radius, height, and slant height form a right triangle,
and the slant height can be calculated using the Pythagorean theorem as .
So, when given and , the lateral surface area of a right circular cone can be calculated as .
With and ,
the slant height is ,
and the lateral surface area is .
I assume that your composite figure is a cone with a hemisphere taken out of the base, so that the cross section looks like this: , and only a ring is left of the base of the cone,like this: .
The surface area of that ring that is left over of the base of the cone
is the area of a circle of radius
minus the area of a circle of radius ; .
The surface area of a sphere of radius is ,
so the surface of a hemisphere of radius is ,
The surface area of your composite figure is mad of three parts:
lateral surface area of the cone = ,
area of ring on the cone base = , and
area of hemisphere = .
Total surface area = .