Pearson Geometry Common Core, 2011
PG
Pearson Geometry Common Core, 2011 View details
6. Surface Areas and Volumes of Spheres
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Exercise 49 Page 739

Let's analyze the given composite solid.

The solid consists of two smaller ones.

  • A cylinder with the radius of cm and a height of cm.
  • A hemisphere with a radius of cm.

We are asked to find the volume and the 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
Therefore, 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,
Substitute values and evaluate
We found that the volume of the composite solid is cubic centimeters.

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,
Therefore, the surface area of the composite solid is square centimeters.