Question

Charles bought a fish tank in the shape of a prism with a base shaped like a regular hexagon. The dimensions of the fish tank are shown below.12 inches30 inchesCharles wants to completely fill the fish tank with water. Which of the following is closest to the number of gallons of water Charles needs to fill the fish tank? (1 gallon231 cubic inches)18.7 gallons48.6 gallons56.1 gallonsO 97.2 gallons

Answer 1

The fish tank is a hexagonal prism, since its base is shaped like a hexagon.

Each side of the hexagonal base measures 12 inches, while the height measures 30 inches.

The volume of the fish tank therefore, is given by the formula;

`\begin{gathered} V=\frac{3\sqrt[]{3}}{2}* a^2* h \\ a=12\text{ (side measure of the base} \\ h=30 \\ V=\frac{3\sqrt[]{3}}{2}*(12)^2*30 \\ V=\frac{3\sqrt[]{3}}{2}*144*30 \\ V=\frac{3\sqrt[]{3}}{2}*4320 \\ V=(3*1.7321)/(2)*4320 \\ V=11224.008in^3 \end{gathered}`

However note that the volume is to be given in gallons, and hence we'll convert cubic inches into gallons.

The standard rate of conversion is

1 cubic inch = 0.004329 gallons.

Therefore, the volume in gallons is, 48.5888 (approximately)