Spheres

A company sells bath oils contained in spherical, water-soluble pods. The circumference of each spherical pod is 14π millimeters. What is the diameter of a pod? The company begins making a smaller version of the bath oil pods. This new version is in the shape of a hemisphere whose great circle has the same length radius as the spherical larger version. What is the surface area of the hemisphere?

14 mm, 147π mm^2

The viewing room at a planetarium is in the shape of a hemisphere. The diameter of the hemisphere is 48 feet. What is the radius of the hemisphere? What is the surface area of the curved viewing surface? What is the total surface area of the hemispheric room? 1,728π ft^2

24 ft, 1,152π ft^2, 1,728π ft^2

The volume of a sphere is (500π)/3 cubic inches. What is the circumference of the great circle of the sphere? (Use 3.14 for pi. Round the answer to the nearest tenth, if necessary. Recall that the formula for the volume for a sphere is v=4/3πr^3 and the formula for the circumference of the great circle is c=πd.)

31.4 in.

The drawing tip of a child's marker is in the shape of a hemisphere. The diameter of the great circle of the hemisphere is 18 millimeters. What is the volume of the drawing tip?

486π cubic millimeters

Part of the North Carolina Museum of Natural Sciences is a model of a three-story globe. Assuming the globe represents a full sphere, the volume of the sphere would be approximately 57,166 2/3π cubic feet. What is the approximate circumference of the globe?

70π feet

The viewing room at a planetarium is in the shape of a hemisphere. The diameter of the hemisphere is 48 feet. What is the volume of the viewing room? A. 9,216π cubic feet B. 18,432π cubic feet C. 73,728π cubic feet D. 147,456 cubic feet

A. 9,216π cubic feet

A company manufactures exercise balls. Type A is a spherical ball with a radius of 12 inches. Type B is a spherical ball with a radius of 16 inches. What is the ratio of the surface area of Type A to the surface area of Type B? A. 9:16 B. 12:16 C. 16:9 D. 16:12

A. 9:16

Mackenzie knows the surface area of a sphere. Which explains how she can find the surface area of a hemisphere with the same radius? A. Divide the surface area of the sphere by 2, and add the area of the base of the hemisphere. B. Multiply the surface area of the sphere by 2, and add the area of the base of the hemisphere. C. Divide the volume of the sphere by 2. D. Multiply the volume of the sphere by 2.

A. Divide the surface area of the sphere by 2, and add the area of the base of the hemisphere.

A piece of solid, spherical glass has a circumference of 3π cm. The sphere is cut in half, creating two identical hemispheres. Geena plans to paint one of the hemispheres to give as a gift. To determine the minimum amount of paint needed, she computes the following. C = 2πr 3π = 2πr r = 1.5 cm SA= ½(4πr2) SA = ½(4π(1.5)2) SA = ½(4π(2.25)) SA = 4.5π cm2 Will Geena have enough paint to cover the entire hemisphere? Why or why not? A. No, she only has enough paint to cover the curved surface. B. No, she only has enough paint to cover the circular base. C. No, she correctly determined the radius, but determined the volume of the hemisphere instead of the surface area. D. Yes, she has enough paint because she found half the area of the surface of the related sphere.

A. No, she only has enough paint to cover the curved surface.

To make a glass marble, 1/6π cm^3 of molten glass is poured into a mold. Jennet finds the circumference of the marble using the steps below. V=4/3πr^3 1/6π=4/3πr^3 1/8=r^3 r=1/2cm c=πr^2 c=1/4π cm^2 Which statements about Jennet's work are true? Check all that apply. A. She correctly determined the radius. B. The radius should be 1 cm. C. The circumference should be π cm. D. The volume should be cm3. E. She used the incorrect volume formula.

A. She correctly determined the radius. C. The circumference should be π cm.

A glass dome for a lighting fixture is in the shape of a hemisphere. The circumference of the great circle of the hemisphere is 12π inches. Which statements about the hemisphere are true? Check all that apply. A. The radius is 6 inches. B. The total surface area is 108π square inches. C. The radius is 12 inches. D. The total surface area is 144π square inches. E. The total surface area is 432π square inches. F. The total surface area is 36π square inches.

A. The radius is 6 inches. B. The total surface area is 108π square inches.

A piece of solid, spherical glass has a circumference of 18.84 centimeters. The sphere is cut in half, creating two identical hemispheres. Using 3.14 for π, Tran computes the amount of paint needed to cover the sphere. C=2πr 18.84=2(3.14)r r=3 cm SA=1/2(4πr^2) SA=2(3.14)(3)^2 SA=56.52 cm^2 A. Tran found the minimum amount of paint needed to cover the curved surface of a hemisphere B. Tran found the minimum amount of paint needed to cover the entire surface of one of the hemispheres. C. Tran found the minimum amount of paint needed to cover both hemispheres. D. Tran found the minimum amount of paint needed to cover the bases of both hemispheres.

A. Tran found the minimum amount of paint needed to cover the curved surface of a hemisphere

A piece of solid, spherical glass has a circumference of 18.84 centimeters. The sphere is cut in half, creating two identical hemispheres. Using 3.14 for π, Tran computes the amount of paint needed to cover the sphere. C=2πr 18.84=2(3.14)r r=3 cm SA=1/2(4πr^2) SA=2(3.14)(3)^2 SA=56.52 cm^2 Which statement about the amount of paint found by Tran is true? A. Tran found the minimum amount of paint needed to cover the curved surface of a hemisphere B. Tran found the minimum amount of paint needed to cover the entire surface of one of the hemispheres. C. Tran found the minimum amount of paint needed to cover both hemispheres. D. Tran found the minimum amount of paint needed to cover the bases of both hemispheres.

A. Tran found the minimum amount of paint needed to cover the curved surface of a hemisphere

To make a glass sphere, 113.04 cm^3 of molten glass is poured into a mold. Using 3.14 for π, Wen finds the circumference of the sphere using the steps below. V=4/3πr^3 113.04=4/3(3.14)r^3 36=4/3r^3 r^3=27 r=9 C=2πr C=18π C=56.52 cm Which statement about Wen's calculations is true? A. Wen incorrectly calculated the radius. B. Wen did not use the correct formula for the circumference. C. Wen should have used the length of the diameter to find the circumference. D. Wen should have used another formula for the volume.

A. Wen incorrectly calculated the radius.

The volume of a sphere is 972π cubic millimeters. What is the circumference of the great circle of the sphere? (Recall that the formula for the volume for a sphere is v=4/3π^3 and the formula for the circumference of the great circle is C=2πr.) A. 9π mm B. 18π mm C. 36π mm D. 162π mm

B. 18π mm

The volume of a sphere is 972π cubic millimeters. What is the circumference of the great circle of the sphere? (Recall that the formula for the volume for a sphere is v=4/3πr^3 and the formula for the circumference of the great circle is C=2πr.) A. 9π mm B. 18π mm C. 36π mm D. 162π mm

B. 18π mm

Ismelda watches a soap bubble resting on a driveway. The bubble is in the shape of a hemisphere. When the bubble pops, the soap residue left behind is in the shape of a circle with the same diameter as the hemisphere. Ismelda measures the diameter of the bubble as 6 inches. What volume of air was in the hemisphere before the bubble popped? (Use 3.14 for π. Round the answer to the nearest tenth, if necessary. Recall that the formula for the volume of a sphere is v=4/3πr^3.) A. 37.7 cu. in. B. 56.5 cu. in. C. 113.0 cu. in. D. 904.3 cu. in.

B. 56.5 cu. in.

A company produces individually wrapped spherical biscuits. The minimum amount of wrapping material needed to cover a biscuit, assuming no edges overlap, is 200.96 square centimeters. What is the diameter of one biscuit? (Use 3.14 for the value of π.) A. 4 cm B. 8 cm C. 16 cm D. 64 cm

B. 8 cm

The radius of a sphere is 8 centimeters. Which formula can be used to find the volume of the sphere? A. V=4/3π(4)^2 B. V=4/3π(8)^3 C. V=4/3π(8)^2 D. V=4/3π(4)^3

B. V=4/3π(8)^3

The volume of a sphere is 81π cubic centimeters. Which equation can be used to solve for the radius of the sphere? A. 81π=4πr^2 B. 81π=4πr^3 C. 81π=4/3πr^3 D. 81π=4/3πr^2

C. 81π=4/3πr^3

A company manufactures exercise balls for gyms. Type A is a spherical ball with a radius of 12 inches. Type B is a hemisphere that will remain stationary when placed on its base. The radius of the hemisphere is also 12 inches. What is the ratio of the surface area of the sphere to the surface area of the hemisphere? A. 2 : 1 B. 3 : 1 C. 3 : 2 D. 4 : 3

D. 4 : 3

The surface area of a sphere is 64π square inches. Which equation can be used to solve for the radius of the sphere? A. 64π = 4πr B. 64π = 2πr3 C. 64π = 2πr2 D. 64π = 4πr2

D. 64π = 4πr2

A hemisphere has a diameter of 26 centimeters. What is the volume of a sphere with the same radius? (Use 3.14 for π. Round the answer to the nearest tenth, if necessary. Recall that the formula for the volume of a sphere is v=4/3πr^3.) A. 2,830.2 cubic centimeters B. 3,066.0 cubic centimeters C. 4,599.1 cubic centimeters D. 9,198.1 cubic centimeters

D. 9,198.1 cubic centimeters

The radius of a hemisphere is 6 inches. Which formula can be used to find the surface area of the hemisphere? A. S = 3π(12)2 B. S = 2π(12)2 C. S = 2π(6)2 D. S = 3π(6)2

D. S = 3π(6)2

The radius of a hemisphere is 6 inches. Which formula can be used to find the surface area of the hemisphere? A. S=3π(12)^2 B. S=2π(12)^2 C. S=2π(6)^2 D. S=3π(6)^2

D. S=3π(6)^2

A piece of solid, spherical glass has a circumference of 37.68 cm. The sphere is cut in half, creating two identical hemispheres. Using 3.14 for π, Sheila computes the amount of paint needed to cover the hemishpheres. C=2πr 37.68=2(3.14)r r=6cm SA=1/2(4πr^2)+πr^2 SA=2π(6)^2+π(6)^2 SA=72(3.14)+36(3.14) SA=339.12 cm^2 Which statement about the amount of paint found by Sheila is true? A. Sheila found the minimum amount of paint needed to cover the curved surface of one of the hemispheres. B. Sheila found the minimum amount of paint needed to cover the bases of both hemispheres. C. Sheila found the minimum amount of paint needed to cover both hemispheres. D. Sheila found the minimum amount of paint needed to cover the entire surface of one of the hemispheres.

D. Sheila found the minimum amount of paint needed to cover the entire surface of one of the hemispheres.

A regulation baseball must have a diameter between 2.87 and 2.94 inches. The surface area of a particular baseball is 9π square inches. Is the baseball within the range of regulation size? Explain your answer.

The baseball is not regulation size. If the baseball has a surface area of 9π, then I can set that equal to the formula 4πr2 and solve for r. The radius is 3/2 inches, so I double that to find the diameter. The diameter of the ball is 3 inches, which is greater than the allowed range of diameters.