Hot air balloons require large amounts of both hot air and fabric material. A hot air balloon is spherical with a diameter of 25 feet
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a. Does finding the surface area help you determine the amount of the hot air or the fabric material? Explain
since the balloon is made of fabric, the surface area is the amount of fabric needed.
Finding the surface area of the hot air balloon can help you determine the amount of fabric material needed.
The fabric material is used to create the envelope, which is the outer shell of the hot air balloon. It needs to be large enough to hold the desired volume of hot air. By calculating the surface area, you can determine how much fabric is required to create this envelope.
To find the surface area of a hot air balloon, you can use the formula for the surface area of a sphere:
Surface Area = 4πr^2
Given that the hot air balloon has a diameter of 25 feet, we can determine the radius by dividing the diameter by 2:
Radius = 25 feet / 2 = 12.5 feet
Plugging this value into the surface area formula, we get:
Surface Area = 4π(12.5^2) = 4π(156.25) = 625π
So, the surface area of the hot air balloon is 625π square feet. This value tells us how much fabric material is needed to create the envelope of the hot air balloon.