McGraw Hill Glencoe Geometry, 2012
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McGraw Hill Glencoe Geometry, 2012 View details
4. Simulations
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Exercise 34 Page 946

To find the area of a hemisphere, calculate the area of half of a sphere with the same radius and add the area of a great circle.

21.2cm^2

Practice makes perfect

A hemisphere is half of a sphere.

Therefore, to find the area of a hemisphere we need to calculate the area of half of a sphere with the same radius and add the area of a great circle. Surface Area of a Hemisphere [0.8em] A=1/2(4Ï€ r^2)+Ï€ r^2 Let's now consider the given diagram.

We know that r is equal to 1.5 centimeters. We can substitute this value in the formula for the area of a hemisphere and simplify.

A=1/2(4Ï€ r^2)+Ï€ r^2
A=1/2(4Ï€ ( 1.5^2))+Ï€ ( 1.5^2)
â–¼
Evaluate right-hand side
A=1/2(4Ï€ (2.25))+Ï€ (2.25)
A=1/2(4(2.25)Ï€ )+2.25Ï€
A=1/2(9Ï€ )+2.25Ï€
A=9/2Ï€+2.25Ï€
A=4.5Ï€+2.25Ï€
A=6.75Ï€
A=21.205750...
A≈ 21.2

The area of the hemisphere to the nearest tenth is 21.2cm^2.