Question

2 (a) Two mathematically similar containers have heights of 30 cm and 75 cm. The larger container has a capacity of 5.5 litres. Calculate the capacity of the smaller container. Give your answer in milliliter

Answer 1

V(small) = 352 milliliters

the capacity of the smaller container is 352 milliliters

Explanation:

Given that the two containers are similar, their dimensions follows the same ratio.

Ratio of their length;

Length(smaller) =30 cm

Length(larger) = 75 cm

Ratio = Length(smaller)/Length(larger) = 30cm/75cm

Length Ratio = 2/5

The ratio of their Volumes will be;

Ratio of volume = ratio of length raised to power three.

Rv = Rl^3

Rv = (2/5)^3

Rv = 8/125

The volume of the smaller container;

V(small) = Rv × V(large)

Volume of larger container V(large) = 5.5 litres

substituting the values;

V(small) = 8/125 × 5.5 litres

V(small) = 0.352 litres

V(small) = 352 milliliters

the capacity of the smaller container is 352 milliliters