Question

1. Main Show Tank Calculation:

Answer 1

Step-by-step explanation:

Volume of a sphere is

$\frac{4}{3} \pi {r}^{3}$

plug in 70 ft for the radius to get 1,436,755 cubic ft then divide that by 4 since the prompt describes a quarter sphere, giving you a tank volume of 359,189 cubic ft.

Volume of a cylinder is

$\pi {r}^{2} h$

from the second prompt we know the tanks are identical since they are said to be congruent which means the hight and radius are the same. Plug in 120 f for h and 35 ft for r to get the volume of a cylinder and then divide that by 2 to get the volume of a single tank. the volume of both tanks would be

$\pi {35}^{2} (120) = 461,814$

To show tank model is a sixth of the original so you divide the radius by 6 and perform the same calculation as in the first portion of the problem ro get the volume a quarter sphere

$\frac{4}{3} \pi {( \frac{70}{6} )}^{3} = 6,652 \: {ft}^{3}$

To get the percentage of the model relative to the original you divide the models volume by the full scale volume

$\frac{6652}{1436755} \times 100 = 0.46$

which is less than 1% of the full scale volume.