McGraw Hill Glencoe Geometry, 2012
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McGraw Hill Glencoe Geometry, 2012 View details
6. Surface Areas and Volumes of Spheres
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Exercise 29 Page 885

Use formula for the volume of a sphere and for the volume of a cylinder.

Volume: About cubic inches
Surface Area: About square inches

Practice makes perfect
Let's analyze the given composite solid.
The solid consists of two smaller ones.
  • A cylinder with a radius of inches, and the height of inches.
  • A hemisphere with a radius of inches.

We are asked to find the volume and surface area of the above solid. First, let's find the volume.

Volume

Let's use the formula for the volume of a sphere and for the volume of a cylinder.

Solid Cylinder Hemisphere
Radius
Height
Volume
The volume of the cylinder is cubic inches and the volume of the hemisphere is cubic inches. Now, let's add these volumes to get the volume of the given composite solid, We will also round the answer to the nearest tenth.
Substitute values and evaluate
We found that the volume of the composite solid is about cubic inches.

Surface Area

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
Height
Area
Now, let's add the area to find the surface area of the composite solid, Then we will round the answer to the nearest tenth.
Substitute values and evaluate
Therefore, the surface area of the composite solid is about square inches.