Question

Volume of hemisphere whos area is 12.5 ft squared

Answer 1

Approximately 6.4 ft³

Explanation:

A *hemisphere* is half of a sphere. As far as surface area goes, we not only need to account for the curved area, but also the area of the circular disc at the bottom. The area of the curved region is going to be half the area of the whole sphere. Since a sphere with radius r has a surface area of 4πr², the curved part of the hemisphere must have half that, or 2πr². Add in the area of the circular disc, πr², and we have a total area of 3πr². Setting this equal to the given area of 12.5 ft², we can solve for r:

`3\pi r^2=12.5\\r^2=12.5/3\pi\\\\r=√(12.5/3\pi)`

Now, using the formula for the volume of a sphere,
`V=(4/3)\pi r^3`, we can substitute our new value for r and solve:

`V=(4/3)\pi r^3\\=(4/3)\pi(√(12.5/3\pi))^3\\\approx 6.4`

Answer 2

radius r = 1.41047396 m

base circumference C = 8.86226925 m

volume V = 5.87697483 m^3

curved surface area A = 12.5 m^2

base surface area B = 6.25 m^2

total surface area K = 18.75 m^2

In Terms of Pi π

base circumference C = 2.82094792 π m

volume V = 1.87069919 π m3

curved surface area A = 3.97887358 π m^2

base surface area B = 1.98943679 π m^2

total surface area K = 5.96831037 π m

Explanation:

• r = radius
• C = base circumference
• V = volume
• A = curved surface area
• B = base surface area
• K = total surface area
• π = pi = 3.1415926535898
• √ = square root

Hemisphere Formulas in terms of radius r:

• Volume of a hemisphere:

V = (2/3)πr^3

• Circumference of the base of a hemisphere:

C = 2πr

• Curved surface area of a hemisphere (1 side, external only):

A = 2πr^2

• Calculate the base surface area of a hemisphere (a circle):

B = πr^2

• Total surface area of a hemisphere:

K = (2πr^2) + (πr^2) = 3πr^2