Volume and Surface Area Problems

Ivan bought a box of macadamia nuts to bring home from his trip. A rectangular prism with a length of 18 centimeters, width of 15 centimeters, and height of 3 centimeters. What volume of nuts could the container hold?

810 centimeters cubed

Marlon built a ramp to put in front of the curb near his driveway so he could get to the sidewalk more easily from the street on his bike. A rectangular prism with a length of 6 inches, width of 18 inches, and height of 6 inches. A triangular prism. The triangular sides have a base of 8 inches and height of 6 inches. The prism has a height of 18 inches. If the ramp includes the flat piece as well as the angled piece and is made entirely out of concrete, what is the total amount of concrete in the ramp?

1,080 inches cubed

Kyle wants to wrap the box in wrapping paper. A rectangular prism with a length of 18 inches, width of 6 inches, and height of 3 inches. What is the minimum amount of paper needed to cover the entire box?

360in2

The top piece from a model of city hall is shown below. A square pyramid. The base is 14 millimeters by 14 millimeters. The triangular sides have a base of 14 millimeters and height of 25 millimeters. The pyramid has a height of 24 millimeters. If Serena painted all the faces of the piece of the model, including the base, what area did she paint?

896 millimeters squared

The cracker manufacturer is trying to determine the best dimensions for the boxes to hold their product so that they use the least amount of cardboard. A rectangular prism with length of 6 inches, width of 4 inches, and height of 12 inches.A rectangular prism with length of 7 inches, width of 6 inches, and height of 9 inches. Which box uses less cardboard, and how much less cardboard does it use? The box on the right uses 30 inches squared less cardboard. The box on the left uses 30 inches squared less cardboard. The box on the right uses 90 inches squared less cardboard. The box on the left uses 90 inches squared less cardboard.

The box on the left uses less cardboard.

Two pyramids like the one below sit on top of the gates at the entrance to the bridge. A square pyramid. The base is 10 inches by 10 inches. The triangular sides have a base of 10 inches and height of 13 inches. The pyramid has a height of 12 inches. Which expression shows how to determine the minimum amount of cement used to make each of the pyramids?

One-third (10) (10) (12)

Mr. Petrov was trying to choose between two different plans for dollhouses for his daughter. Both dollhouses have a rectangular prism base with a length of 6 inches, width of 6 inches, and height of 5 inches. Dollhouse 1 has a triangular prism top. The triangular base has a base of 6 inches and height of 4 inches. The prism has a height of 6 inches. Dollhouse 2 has a square pyramid top with a base of 6 inches by 6 inches and height of 4 inches. Which statements are true about the dollhouses? Select three options. The space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4). The space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-third (6) (6) (4). The space inside dollhouse 2 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4). The space inside dollhouse 2 can be found using the equation V = 6 (6) (5) + one-third (6) (6) (4). The space inside dollhouse 1 is 24 inches cubed greater than the space inside dollhouse 2.

1,4,5

Hiro bought a small carton of milk at lunch. A rectangular prism with length of 3 inches, width of 3 inches, and height of 6.5 inches. A triangular prism. The triangular side has a base of 3 inches and height of 1.5 inches. The prism has a height of 3 inches. If the approximate dimensions of the milk carton are shown, what is the minimum amount of cardboard needed to make the milk carton? Round to the nearest whole number.

104 in 2

The hood above the stove in a restaurant kitchen is filled with fans and other ventilation parts. A triangular prism. The triangular sides have a base of 3 feet and height of 2 feet. The prism has a height of 4 feet. How much space is there inside the empty hood?

12 ft3

The approximate measurements of the Great Pyramid of Khufu are shown below. A square pyramid. The base is 230 meters by 230 meters. The triangular sides have a base of 230 meters and height of 187 meters. The pyramid has a height of 147 meters. What is the surface area of the pyramid?

138,920 meters squared

Polina has a glass vase in the shape of a rectangular prism with an open top, as shown below. A rectangular prism with a length of 4 inches, width of 3.5 inches, and height of 10 inches. What is the maximum amount of water that the vase can hold?

140 in.3

Anderson's Nursery was choosing between two different greenhouses. 2 greenhouses have a rectangular prism base with a length of 12 meters, width of 12 meters, and height of 10 meters. Greenhouse 1 has a square pyramid top with a base of 12 meters by 12 meters and height of 8 meters. Greenhouse 2 has a triangular prism top. The triangular sides have a base of 12 meters and height of 8 meters. The prism has a height of 12 meters. Which statements are true about the greenhouses? Select two options. The space inside greenhouse 1 can be found using the equation V = 12 (12) (10) + one-half (12) (12) (8). The space inside greenhouse 1 can be found using the equation V = 12 (12) (10) + one-third (12) (12) (8). The space inside greenhouse 2 can be found using the equation V = 12 (12) (10) + one-half (12) (12) (8). The space inside greenhouse 2 can be found using the equation V = 12 (12) (10) + one-third (12) (12) (8). The space inside greenhouse 1 is 192 meters cubed greater than the space inside greenhouse 2.

2, 3

Morgan's mother won a solid glass award at work with the dimensions below. A rectangular prism with length 18 centimeters, width 18 centimeters, and height 3 centimeters. A square pyramid with a base of 18 centimeters by 18 centimeters and height of 40 centimeters. The triangular sides have a base of 18 centimeters and height of 41 centimeters. If the award was wrapped in cellophane when it arrived, what is the minimum amount of cellophane that was used?

2016cm2

A metronome is a device that ticks at adjustable intervals to help keep time when playing music. The metronome on Ryan's piano has the basic shape below. A square pyramid. The base is 9 centimeters by 9 centimeters. The triangular sides have a base of 9 centimeters and height of 20.5 centimeters. The pyramid has a height of 20 centimeters. If the metronome was created out of a piece of solid wood, what is the minimum amount of solid wood that was used?

540cm3

The cloth top of the gazebo in Mr. Chang's backyard has ripped from weathering. He needs to know the area of the cloth so he can replace it. A square pyramid with a base of 6 feet by 6 feet. The triangular sides have a height of 5 feet. The height of the pyramid is 4 feet. How much cloth, in square feet, will Mr. Chang need, assuming he does not need to replace the cloth at the bottom of the figure?

60

Bob bought a solid rubber doorstop to keep the air flowing between the rooms of his apartment. A triangular prism. The triangular sides have a base of 2 centimeters and height of 1.5 centimeters. The prism has a height of 5 centimeters. What is the minimum amount of rubber used to make the doorstop?

7.5 cm3