Question

An igloo can be modeled as a hemisphere. Its circumference measures 20.9 m. Find its volume in cubic meters. Round your answer to the nearest tenth

Answer 1

To find the volume of the hemisphere, calculate the radius using the circumference formula and then use the volume formula for a hemisphere.

Step-by-step explanation:

To find the volume of the hemisphere, we need to first calculate the radius. The circumference of the hemisphere is given to be 20.9 m. We can use the formula for circumference, C = 2πr, where C is the circumference and r is the radius. By rearranging the formula, we find that the radius is 20.9 m / (2π) = 3.32 m (rounded to two decimal places).

Next, we can use the formula for the volume of a hemisphere, V = (2/3)πr³, where V is the volume and r is the radius. Plugging in the radius, we get V = (2/3)π(3.32 m)³ ≈ 85.8 m³ (rounded to one decimal place).

Therefore, the volume of the igloo, modeled as a hemisphere, is approximately 85.8 cubic meters.

Answer 2

To calculate the volume of the igloo modeled as a hemisphere, the radius was first determined from the given circumference and then the volume formula for a hemisphere [V = (2/3)πr³] was applied, yielding a volume of approximately 77.5 cubic meters.

Step-by-step explanation:

To find the volume of an igloo modeled as a hemisphere, we need to use the information given about the circumference to first determine the radius of the hemisphere. The formula for the circumference (C) of a circle (which applies to our hemisphere's base) is C = 2πr, where π (pi) is approximately 3.14159 and r is the radius.

To isolate the radius (r), we will rearrange the formula to get r = C / (2π). Substituting the given circumference (20.9 m) into the formula gives us r = 20.9 m / (2 × 3.14159), which calculates to approximately 3.33 meters (rounded to two decimal places for intermediate calculations).

After finding the radius, we can calculate the volume (V) of a hemisphere using the formula V = (2/3)πr³. By substituting the radius (3.33 m) into this formula, we find the volume to be about (2/3) × 3.14159 × (3.33 m)³, which equals approximately 77.5 cubic meters when rounded to the nearest tenth.