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Find the surface area and the volume for the following spheres and hemispheres. 7. 8. 9. 2 12 5

Find the surface area and the volume for the following spheres and hemispheres. 7. 8. 9. 2 12 5

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Leave answers in terms of pi by using "pi" or round to the nearest 10th.    If using pi in a fraction, be sure that it is in the numerator: example 4pi/3

**Find the Surface Area and the Volume for the Following Spheres and Hemispheres** For each of the problems below, leave your answers in terms of \(\pi\) by using "pi" or round to the nearest 10th. If using \(\pi\) in a fraction, be sure that it is in the numerator. For example: \( \frac{4\pi}{3} \). **Problems:** 7. Sphere with a radius of 5 units. - Diagram: A sphere labeled with the radius of 5 units. 8. Hemisphere with a radius of 2 units. - Diagram: A hemisphere labeled with the radius of 2 units. 9. Sphere with a diameter of 12 units. - Diagram: A sphere labeled with the diameter of 12 units. Calculate the surface area and the volume for each problem using the appropriate formulas for spheres and hemispheres. **Formulas:** - Volume of a sphere: \( V = \frac{4}{3} \pi r^3 \) - Surface area of a sphere: \( A = 4 \pi r^2 \) - Volume of a hemisphere: \( V = \frac{2}{3} \pi r^3 \) - Surface area of a hemisphere: \( A = 2 \pi r^2 \) (not including base) or \( A = 3 \pi r^2 \) (including base) Use these formulas to solve the given problems.
Transcribed Image Text:**Find the Surface Area and the Volume for the Following Spheres and Hemispheres** For each of the problems below, leave your answers in terms of \(\pi\) by using "pi" or round to the nearest 10th. If using \(\pi\) in a fraction, be sure that it is in the numerator. For example: \( \frac{4\pi}{3} \). **Problems:** 7. Sphere with a radius of 5 units. - Diagram: A sphere labeled with the radius of 5 units. 8. Hemisphere with a radius of 2 units. - Diagram: A hemisphere labeled with the radius of 2 units. 9. Sphere with a diameter of 12 units. - Diagram: A sphere labeled with the diameter of 12 units. Calculate the surface area and the volume for each problem using the appropriate formulas for spheres and hemispheres. **Formulas:** - Volume of a sphere: \( V = \frac{4}{3} \pi r^3 \) - Surface area of a sphere: \( A = 4 \pi r^2 \) - Volume of a hemisphere: \( V = \frac{2}{3} \pi r^3 \) - Surface area of a hemisphere: \( A = 2 \pi r^2 \) (not including base) or \( A = 3 \pi r^2 \) (including base) Use these formulas to solve the given problems.
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