Notice that you only need to know the radius of a sphere to find its volume and surface area. This means that if you know the volume of a sphere, you can find its surface area.
Problem 4 Using Volume to Find Surface Area
The volume of a sphere is
| Know | Need | Plan |
|---|---|---|
| The volume of a sphere | The radius of the sphere | Work backward by using the formula for volume and solving for r. Then use the radius to calculate surface area. |
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Step 1 Find the radius of the sphere.
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Step 2 Find the surface area of the sphere.
The surface area of the sphere is about
✓ Got It?
- The volume of a sphere is
✓ Lesson Check
Do you know HOW?
The diameter of a sphere is 12 ft.
- What is its surface area in terms of π?
- What is its volume to the nearest tenth?
- The volume of a sphere is
Do you UNDERSTAND?
- Vocabulary What is the ratio of the area of a great circle to the surface area of the sphere?
- Error Analysis Your classmate claims that if you double the radius of a sphere, its surface area and volume will quadruple. What is your classmate's error? Explain.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs