Question

17. Two tanks are similar in shape. The capacity of the tanks are 1,000,000 litres and 512, 000 liters respectively

Answer 1

Given that, Two tanks are similar in shape. The capacity of the tanks are 1,000,000 litres and 512, 000 liters respectively.Find the height of the smallest tank if the larger is 300cm tall?

Assume that, the tanks are rectangular in shapes and differ only on their heights. The volume of the larger tank is

V1 = l × w × h1 while the volume of the smaller tank is V2 = l ×w × h2. The ratios of the capacities is

$\sf \frac{V1}{V2} = l \times w \times h1 \times w \times h2 = \frac{h1}{h2}$

Solving for the height of the smaller tank h2

$\sf \frac{V1}{V2} = \frac{h1}{h2}$

$\sf\frac{1000000} {51200} = \frac{ 300 cm }{ h2}$

1000000 × h2 = 51200 × 300 cm

h2 = (51200 × 300 cm) /1000000

h2 = 15.36 cm

$\sf\implies \: \boxed{ \bf{ \: Height \: of \: the \: smaller \: tank \: is \: 15.36 cm.\: }}$

${ \underline {\rule{5000pt}{6pt}}}$

Answer 2

Because the tanks are similar in shape we can use scale factors
The scale factor for volume = 512000/1000000 = 0.512
Volumes are a cubic measure
The linear scale factor = cube root(0.512) = 0.8
If the height of the big tank is 300cm then the smaller tank height = 300 x 0.8 = 240cm