Everything Maths Grade 10

Dimensions Volume Surface

Multiply two dimensions by 5

5 h

b

5 l

V 2 = 5lb 5 h

= 5:5 (lbh)

= 5^2 V

A 2 = 2 [(5l 5 h) + (5lb) + (b 5 h)]

= 25 (5lh+lb+bh)

Multiply all three dimensions by

5

5 h

5 l 5 b

V 3 = 5l 5 b 5 h

= 5^3 (lbh)

= 5^3 V

A 3 = 2 [(5l 5 h) + (5l 5 b) + (5b 5 h)]

= 2

(

52 lh+ 5^2 lb+ 5^2 bh

)

= 5^2 2 (lh+lb+bh)

= 5^2 A

Multiply all three dimensions by

k

kh

kl kb

Vk =klkbkh

=k^3 (lbh)

=k^3 V

Ak = 2 [(klkh) + (klkb) + (kbkh)]

=k^2 2 (lh+lb+bh)

=k^2 A

Worked example 18: Calculating the new dimensions of a rectangular prism

QUESTION

Consider a rectangular prism with a height of 4 cm and base lengths of 3 cm.

4 cm

3 cm 3 cm

1.Calculate the surface area and volume.

2.Calculate the new surface area (An) and volume (Vn) if the base lengths are multiplied by a constant

factor of 3.

3.Express the new surface area and volume as a factor of the original surface area and volume.

452 13.4. The effect of multiplying a dimension by a factor ofk