topic badge
Hong Kong
Stage 1 - Stage 3

Surface Area of Complex Composite Solids


As we saw in earlier chapters on Surface Area of Composite shapes, the methods for calculating the surface area is to calculate the areas of each face and add them up.  You may have faces that are equal in size, and therefore will have equal area. Don't forget to subtract faces which are not on the surface and another common mistake is when faces that are not able to be seen are forgotten, (like those on the bottom or back of a 3D image).  

We have a lot of 3D shapes covered so far, 

Prisms, Right Pyramids, Right Cones, Spheres and Cylinders.  Your composite shapes could have any combination of these shapes within them!

The best way to see composite shapes in action is through some examples.


Question 1

Find the surface area of the composite figure shown, which consists of a cone and a hemisphere joined at their bases.

Round your answer to two decimal places.

A composite figure consisting of a hemisphere and a cone that are conjoined at their bases. The flat base of the hemisphere serves as the circular base of the cone. The composite figure is oriented vertically, with the apex of the cone directed upward.
A vertical dashed line extending from the cone’s apex to the center of its base measures $10$10 cm. A horizontal dashed line is also drawn from the center of the cone's base to its circumference and measures $4$4 cm. These two dashed lines intersect at a right angle, indicated by a small square at the intersection point.

Question 2


Find the surface area of the composite figure shown.

Round your answer to two decimal places.




What is Mathspace

About Mathspace