6. Surface Areas and Volumes of Spheres
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Let's analyze the given composite solid.
The solid consists of two smaller ones.
We are asked to find the volume and the surface area of the above solid. First, let's find the volume.
Let's use the formula for the volume of a sphere and for the volume of a cylinder.
Solid | Cylinder | Hemisphere |
---|---|---|
Radius | r=2 | r=2 |
Height | h=2.5 | − |
Volume | V=πr2h | V=21⋅34πr3 |
V1=π(2)2(2.5)=10π | V2=21⋅34π(2)3=316π |
V1=10π, V2=316π
ca⋅b=ca⋅b
a=33⋅a
Multiply
Add fractions
ca⋅b=ca⋅b
Now, we will find the surface area of the given composite solid. Notice that it is equal to the surface area of the hemisphere, the lateral area of the cylinder, and one base area of the cylinder. Let's use the formulas for the surface area of a sphere and for the surface area of a cylinder.
Surface | Hempishere | Lateral Area of Cylinder | Base Area of Cylinder |
---|---|---|---|
Radius | r=2 | r=2 | r=2 |
Height | h=2.5 | − | − |
Area | A=21⋅4πr2 | A=2πrh | A=πr2 |
A1=21⋅4π(2)2=8π | A2=2π(2)(2.5)=10π | A3=π(2)2=4π |