Question

A hemisphere igloo has the volume of 9,202.8 meters cubed. What is the area of the floor of the igloo.

Answer 1

2527.43 square meters

Explanations:

The formula for calculate the volume of hemisphere is given as:

`v=(2)/(3)\pi r^3`

where"r" is the radius of the hemisphere

Given the following parameters:

• V = 9,202.8 meters cubed.

Substitute the given parameters into the formula to get the radius:

`\begin{gathered} 9202.8=(2)/(3)*3.14* r^3 \\ 9202.8*3=2*3.14* r^3 \\ 27608.4=6.28r^3 \\ r^3=4396.24 \\ r=\sqrt[3]{4396.24} \\ r\approx16.38m \end{gathered}`

Determine the area of the floor given the radius above:

`\begin{gathered} A=3\pi r^2 \\ A=3(3.14)*(16.38)^2 \\ A=2527.43m^2 \end{gathered}`

Hence the area of the floor of the igloo is 2527.43 square meters