Estimating Volumes

A person just purchased a vending machine with three compartments. Each compartment has the dimensions of 6 inches by 8 inches by 18 inches. Assuming the vending machine uses gumballs that are approximately spherical and 2 inches in diameter, how many gumballs should fit in one of the compartments?

(Hint: Packing spheres in a rectangular prism usually take up 190% of the volume of spheres.)

• 108

• 13

• 54

• 206

Approximately 15 tennis balls can fill the inside of a cardboard box with the following dimensions: 5 in x 6 in x 10 in. If my classroom is 10 feet high, 32 feet wide, and 25 feet long, estimate the number of tennis balls required to fill my classroom. (Hint: 1 feet= 12 inches)

• 400

• 691200

• 4800

• 46080

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

Approximately 5 tennis balls can fill the inside of a cardboard box with the following dimensions: 5 in x 5 in x 10 in. If my classroom is 10 feet high, 28 feet wide, and 20 feet long, estimate the number of tennis balls required to fill my classroom. (Hint: 1 feet= 12 inches)

• 128,937

• 1344

• 193,536

• 93,785

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

A person is using a new tennis ball launching machine that is 12 inches by 15 inches by 10 inches. Assuming the machines uses tennis balls that are spherical and 1.8 inches in diameter, how many tennis balls should fit in the top of the machine? (Hint: Packing spheres in a rectangular prism usually take up 190% of the volume of the spheres using random packing and the following formula volume of a sphere is).

• 310

• 589

• 73

• 38

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Approximately 32 tennis balls can fill the inside of a cardboard box with the following dimensions: 5 in x 15 in x 12 in. If my classroom is 10 feet high, 38 feet wide, and 20 feet long, estimate the number of tennis balls required to fill my classroom. (Hint: 1 feet= 12 inches)

• 82,092

• 76,348

• 72,456

• 70,314

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

A basketball has a diameter of 16.8 . How many basketballs will fit inside of a room that is 14 feet wide, 10 long, and 6 feet high? (Hint: Packing spheres in a rectangular prism usually take up 190% of the volume of the spheres using random packing and the following formula volume of a sphere is).

• 2461

• 4677

• 330

• 32

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Approximately 14 gumballs can fill the inside of a cardboard box with the following dimensions:

9 in x 1 in x 2 in. If my classroom is 12 inches high, 28 inches wide, and 15 inches long, estimate the number of gumballs required to fill my vending machine. (Hint: 1 feet= 12 inches)

• 3920

• 6,773,760

• 47,040

• 10,280

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

A person is purchasing a new golf club bag. The compartment for the golf balls is approximately the shape of a rectangular prism with the dimensions of 10 inches by 12 inches by 6 inches. Assuming golf balls are spherical with a 2.3-inch diameter, how many golf balls should fit in the compartment bag? (Hint: Packing spheres in a rectangular prism usually take up 190% of the volume of the spheres using random packing and the following formula volume of a sphere is).

• 59

• 50

• 73

• 90

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3