Everything Maths Grade 10

Worked example 16: Finding the volume of a complex object

QUESTION

A triangular pyramid is placed on top of a triangular prism, as shown below. The base of the prism is an
equilateral triangle of side length 20 cm and the height of the prism is 42 cm. The pyramid has a height of
12 cm. Calculate the total volume of the object.

12 cm

20 cm

42 cm

SOLUTION

Step 1: Calculate the volume of the prism

First find the height of the base triangle using the theorem of Pythagoras:

10 cm

hb

20 cm

202 = 10^2 +h^2 b

)hb=

√

202 102

= 10

p

3 cm

Next find the area of the base triangle:

area of base triangle=

1

2

 20  10

p

3

= 100

p

3 cm^2

446 13.3. Right pyramids, right cones and spheres