Geometry Volume and Scale Factor

It takes 6 cubic inches of colored sand to fill a plastic cone. How many cubic inches will it take to fill a plastic cylinder with the same base and height as the cone?

• 2

• 12

• 18

• 24

and Δ DEF are shown on the coordinate grid below. Which series of transformations describes one way that Δ DEF could be transformed to produce Δ ABC?

• a dilation from the origin using a scale factor of 2, a reflection across the x-axis, and then a translation 10 units to the left

• a dilation from the origin using a scale factor of 3, a reflection across the x-axis, and then a translation 10 units to the left

• a dilation from the origin using a scale factor of 2, a reflection across the y-axis, and then a translation 4 units up

• a dilation from the origin using a scale factor of 3, a reflection across the y-axis, and then a translation 4 units up

A silo is a building shaped like a cylinder used to store grain. The diameter of a particular silo is 6.5 meters, and the height of the silo is 12 meters. Which equation can be used to find V, the volume of this silo in cubic meters?

Snacks at a county fair are sold in containers shaped like a cone or a cylinder. The dimensions of each container are shown in the drawing. Which statement about the volumes of the cone and cylinder is true?

• The volume of the cylinder is about 377 cubic inches greater than the volume of the cone.

• The volume of the cylinder is about 377 cubic inches less than the volume of the cone.

• The volume of the cylinder is about 25 cubic inches greater than the volume of the cone.

• The volume of the cylinder is about 25 cubic inches less than the volume of the cone.

A cone and ints dimensions are shown in the diagram. Which measurement is closest to the volume of the cone in cubic inches?

• 186.38 in³

• 248.50 in³

• 745.51 in³

• 62.13 in³

If the area of the blue square is 25 in² and the area of the green square is 169 in², what is the area of the yellow square?

• 12 in²

• 144 in²

• 194 in²

• 13.9 in²

A sphere and its dimensions are shown in the diagram. Which measurement is closest the the volume of the sphere in cubic inches?

• 1,325.4 in³

• 188.5 in³

• 94.2 in³

• 1,767.1 in³

Enlargement or reduction?  Find the scale factor!

• It's a reduction; the scale factor is 2.

• It's an enlargement; the scale factor is 2.

• It's an enlargement; the scale factor is 1/2.

• It's a reduction; the scale factor is 1/2.

Triangle PQR is similar to triangle DEF shown. Which describes the relationship between the corresponding sides of the two triangles?

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• 
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A triangle with vertices T(0,0), U (0,3), and V (4,0) is dilated, and the vertices of the new triangle are T' (0,0), U' (0, 1.5), and V' (2, 0). which best represents the scale factor applied to the original triangle?

• (1x, 1y)

• (0x, 0y)

• (0x, -0.5y)

• (0.5x, 0.5y)