Everything Maths Grade 10

SOLUTION

Step 1: Calculate the original volume and surface area

V=r^2 h

A=r^2 + 2rh

Step 2: Calculate the new volume and surface area

The new dimensions arekrandh.

Vn=(kr)^2 h

=k^2 r^2 h

=k^2 r^2 h

=k^2 V

An=(kr)^2 + 2(kr)h

=k^2 r^2 + 2krh

=k^2

(

r^2

)

+k(2rh)

Exercise 13 – 6:

1.If the length of the radius of a circle is a third of its original size, what will the area of the new circle be?

r

2.If the length of the base’s radius and height of a cone is doubled, what will the surface area of the new

cone be?

r

H

h

3.If the height of a prism is doubled, how much will its volume increase by?

4.Describe the change in the volume of a rectangular prism if the:

a)length and breadth increase by a constant factor of 3.

b)length, breadth and height are multiplied by a constant factor of 3.

Chapter 13. Measurements 455