Math / Geometry

QuestionA tank is a vertical cylinder with inside diameter of 6 ft and a height of 15 ft :
10. What is the volume of liquid in cubic feet if we fill the tank to one foot high? A. $28.27 \mathrm{ft}^{3}$ B. $18.8 \mathrm{ft}^{3}$ C. $113.1 \mathrm{ft}^{3}$ D. $424.1 \mathrm{ft}^{3}$
11. What is the total volume of the tank in cubic feet? A. $1686.5 \mathrm{ft}^{3}$ B. $442.5 \mathrm{ft}^{3}$ C. $424.1 \mathrm{ft}^{3}$ D. $847.5 \mathrm{ft}^{3}$

Studdy Solution
Substitute the values to find the total volume of the tank when the height $h$ is $15$ feet:
$V = \pi (3 \text{ ft})^2 (15 \text{ ft})$ $= \pi \times 9 \text{ ft}^2 \times 15 \text{ ft}$ $= 135\pi \text{ ft}^3$
Using $\pi \approx 3.14159$ :
$V \approx 135 \times 3.14159 \text{ ft}^3$ $\approx 424.11 \text{ ft}^3$
The total volume of the tank is:
$\boxed{424.1 \text{ ft}^3}$

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