Apply Similarity Theorems

Marty is making props for the school play that are right cylinders. He originally designs the cylinders to be 5 feet tall, but the cost of the fabric to wrap around the sides of the cylinders will be too expensive. The play's producer asks Marty to reduce the dimensions proportionally so that the cylinders are 2 feet tall.

By what percentage should Marty multiply his estimate for the amount of the fabric in order to give the producer an accurate idea of the new cost?

The smaller cylinder's surface area is ___ % of the surface area of the larger cylinder.

The smaller cylinder shown in the diagram has a radius of 4 inches and a height of 8 inches. The larger cylinder has a radius of 6 inches and a height of 12 inches.

Which statement about the surface area of the cylinders is true?

• The two cylinders are not proportional, so you cannot calculate the surface area of the larger cylinder as a multiple of the smaller.

• The two cylinders are proportional, and the surface area of the larger cylinder is larger by a factor of 9/4.

• The two cylinders are proportional, and the surface area of the larger cylinder is larger by a factor of 2.

• The two cylinders are proportional, and the surface area of the larger cylinder is larger by a factor of 4.

Jamie is designing a model for art class. The model is a cube-shaped box with a circular image on one face of the box.

She creates the design with a smaller scale model before building the full-size piece. The smaller scale model of the cube has edge lengths each measuring 4 centimeters, and the circular image has an area of 9π square centimeters.

How large will the cube need to be in the full-size art piece so that the circular image will have an area of 36π square centimeters?

Each edge of the cube should be ____ centimeters.

Tags

CCSS.7.G.A.1

The diagram shows two similar pyramids. The larger one has a volume of 2,197 cubic centimeters. The smaller one has a volume of 729 cubic centimeters.

What is the ratio of their heights?

• 1.5:1

• 4:3

• 13:9

• 169:81

• 2,197:729

Jerry is using a computer program to design a 24-ounce bottle for a natural juice company. The cost of materials to produce the juice bottles is determined by the surface area of the bottles, and the design for the 24-ounce bottle has 100 square inches of surface area.

The juice company also wants Jerry to scale his design to fit 40 ounces of juice.

What will be the surface area of the 40-ounce bottle?

• 108 square inches

• 120.3 square inches

• 133.3 square inches

• 140.6 square inches

• 166.7 square inches

A sculpture is made of two similar cones with parallel bases, joined at their tips. The sculpture is 15 inches tall, and its base is 12 inches in diameter. If the ratio of the volumes of the two cones is 8:27, how many inches from the base of the sculpture is the meeting point of the cones?

The point is ____ inches above the base of the sculpture.

Lily works in the kitchen-supply section at a department store. She notices that the small “home-size” funnel, 8 inches tall, can hold 12 fluid ounces. She measures a larger “restaurant-size” funnel, similar in shape, and finds that it is 18 inches tall.

How many fluid ounces can it hold?

The larger funnel can hold _____ fluid ounces. Express your answer to the nearest tenth of a fluid ounce.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Laurie is attending a French pastry school. She generally uses a large cone-shaped bag to squeeze icing onto her cakes.

Today, another student was using the larger bag, so Laurie is using a similar cone-shaped bag that is half as big in each dimension.

How many times will Laurie need to fill the smaller bag to decorate the same size cake that the larger bag could do with one filling?

Laurie will need to fill the smaller bag ____ times.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

9.

An enlarger is a device used to make prints from photographic negatives by casting light through the film onto special paper. The greater the distance the film is from the paper, the bigger the image projected onto the paper by the enlarger.Based on the diagram and the assumption that the pyramids of light are similar, at approximately what height should you set the enlarger to create an 8 inch by 10 inch image on the photo paper?

• 33 inches

• 30.5 inches

• 30 inches

• 19.2 inches

• 17.5 inches

Tags

CCSS.HSG.SRT.B.5

Examine the pairs of objects below. Determine whether the two objects in each pair are similar or not. Select all of the similar objects.

Select the objects by clicking on the tile.

• 
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• 
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Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6