Everything Maths Grade 10

Now we can find the volume of the prism:

)volume of prism=area of base triangleheight of prism

= 100

p

3  42

= 4200

p

3 cm^3

Step 2: Calculate the volume of the pyramid

The area of the base triangle is equal to the area of the base of the pyramid.

)volume of pyramid=

1

3

(area of base)H

=

1

3

 100

p

3  12

= 400

p

3 cm^3

Step 3: Calculate the total volume

total volume= 4200

p

3 + 400

p

3

= 4600

p

3

=7967,4 cm^3

Therefore the total volume of the object is 7967,4 cm^3.

Worked example 17: Finding the surface area of a complex object

QUESTION

With the same complex object as in the previous example, you are given the additional information that the
slant heighths= 13,3 cm. Now calculate the total surface area of the object.

SOLUTION

Step 1: Calculate the surface area of each exposed face of the pyramid

area of one pyramid face=

1

2

bhs

=

1

2

 20 13,3

=133 cm^2

Because the base triangle is equilateral, each face has the same base, and therefore the same surface area.
Therefore the surface area for each face of the pyramid is 133 cm^2.

Step 2: Calculate the surface area of each side of the prism

Each side of the prism is a rectangle with baseb=20 cm and heighthp=42 cm.

Chapter 13. Measurements 447