11-6 Surface Areas and Volumes of Spheres

Quick Review

The surface area of a sphere is four times the product of π and the square of the radius of the sphere. The volume of a sphere is 4 3 4 thirds  the product of π and the cube of the radius of the sphere.

Example

What is the surface area of a sphere with radius 7 ft? Round your answer to the nearest tenth.

S . A . = 4 π r 2 Use the formula for surface area of a sphere.   = 4 π ( 7 ) 2 Substitute.   ≈ 615.8 Simplify. table with 3 rows and 4 columns , row1 column 1 , cap s . cap a . , column 2 equals , column 3 4 pi , r squared , column 4 cap use the formula for surface area of a sphere. , row2 column 1 , , column 2 equals , column 3 4 pi . open 7 , close squared , column 4 cap substitute. , row3 column 1 , , column 2 almost equal to , column 3 615.8 , column 4 cap simplify. , end table

The surface area of the sphere is about 615.8 ft 2 . 615.8 . ft squared , .

Exercises

Find the surface area and volume of a sphere with the given radius or diameter. Round your answers to the nearest tenth.

25. r = 5  in. r equals 5 , in.
26. d = 7  cm d equals 7 cm
27. d = 4  ft d equals 4 ft
28. r = 0.8  ft r equals 0.8 , ft
29. What is the volume of a sphere with a surface area of 452.39  cm 2 ? 452.39 . cm squared , question mark  Round your answer to the nearest hundredth.
30. What is the surface area of a sphere with a volume of 523.6  m 3 ? 523.6 . m cubed , question mark  Round your answer to the nearest square meter.
31. Sports Equipment The circumference of a lacrosse ball is 8 in. Find its volume to the nearest tenth of a cubic inch.

11-7 Areas and Volumes of Similar Solids

Quick Review

Similar solids have the same shape and all their corresponding dimensions are proportional.

If the scale factor of two similar solids is a : b, then the ratio of their corresponding surface areas is a 2 : b 2 , eh squared , colon , b squared , comma  and the ratio of their volumes is a 3 : b 3 . eh cubed , colon , b cubed , .

Example

Is a cylinder with radius 4 in. and height 12 in. similar to a cylinder with radius 14 in. and height 35 in.? If so, give the scale factor.

4 14 ≠ 12 35 4 fourteenths , not equal to , 12 over 35

The cylinders are not similar because the ratios of corresponding linear dimensions are not equal.

Exercises

32. Open-Ended Sketch two similar solids whose surface areas are in the ratio 16 : 25. Include dimensions.

For each pair of similar solids, find the ratio of the volume of the first figure to the volume of the second.

33. 
34. 
35. Packaging There are 12 pencils in a regular-sized box. If a jumbo box is made by tripling all the dimensions of the regular-sized box, how many pencils will the jumbo box hold?

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