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Use formula for the volume of a sphere and for the volume of a cylinder.
Volume: 623Ď€ cubic centimeters
Surface Area: 26Ď€ square centimeters
Let's analyze the given figure.
The solid consists of three 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=Ď€ r^2 h | V=1/2*4/3Ď€ r^3 |
V_1=Ď€ ( 2)^2( 2.5)= 10Ď€ | V_2=1/2*4/3Ď€ ( 2)^3= 16/3Ď€ |
V_1= 10Ď€, V_2= 16/3Ď€
a/c* b = a* b/c
a*b/c= a* b/c
a = 3* a/3
Multiply
Add fractions
a* b/c=a/c* b
Now, we will find the surface area of the given composite solid. Notice that it is equal to the surface area of two hemispheres and the lateral 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 |
---|---|---|
Radius | r= 2 | r= 2 |
Height | h= 2.5 | - |
Area | A=1/2* 4Ď€ r^2 | A=2Ď€ r h |
A_1=1/2* 4Ď€ ( 2)^2= 8Ď€ | A_2=2Ď€( 2)( 2.5)= 10Ď€ |
Substitute values
Multiply
Add terms