Milestones Review - 7th grade Geometry

A bicycle training wheel has a radius of 3 inches. The bicycle wheel has a radius of 10 inches. Approximately how much smaller, in square inches and rounded to the nearest hundredth, is the area of the training wheel than the area of the regular wheel?

• 21.98

• 153.86

• 285.74

• 1,142.96

Answer explanation

Area of a circle can be find by doing πr². In order to solve this problem, you must find the area of the training wheel an the area of the actual wheel and then subtract your two answers.

Tags

CCSS.7.G.B.4

Select all of the cross-sections that can occur when slicing a cone.

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Answer explanation

A cone can be sliced perpendicular to the base (meaning it will match the sides and be a triangle), parallel to the base (meaning it will match the base and be a circle), or a slanted slice (resulting in ovals, ellipse, etc.)

Tags

CCSS.7.G.A.3

Select all of the cross-sections that can occur when slicing a cube.

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Answer explanation

A cube can be sliced perpendicular to the base (meaning it will match the sides and be a square), parallel to the base (meaning it will match the base and be a square), or a slanted slice (resulting in trapezoids, triangles, rectangles, etc.)

Tags

CCSS.7.G.A.3

Consider the diagram of supplementary angles.

What is the value of χ?

• 10.4

• 52

• 61.6

• 92

Answer explanation

Supplementary angles add up to 180°. In order to solve for x, you set up a two step equation: 5x + 128 = 180. Subtract 128 from 180 and then divide your answer by 5.

Tags

CCSS.7.G.B.5

Consider the graph of two rectangular prisms. What is the volume of this figure in cubic inches?

• 32

• 256

• 416

• 7,680

Answer explanation

Find the volume of each of the prisms by doing V=Bh or l⋅w⋅h and add your two answers together.

Tags

CCSS.5.MD.C.5C

A circular rug has a diameter of 12 feet.

What is the circumference, in feet, of the rug rounded to the nearest hundredth? Use 3.14 for π.

Answer explanation

Circumference of a circle can be solved by doing C=πd

Tags

CCSS.7.G.B.4

A circular rug has a diameter of 12 feet.

What is the area, in feet, of the rug rounded to the nearest hundredth? Use 3.14 for π.

Answer explanation

Area of a circle can be solved by doing A=πr². Since you are only given the diameter, you must first 1/2 that to get the radius and then square your radius and multiply it by 3.14

Tags

CCSS.7.G.B.4

What is the range for the third possible side of a triangle with 2 side lengths of 3 cm, 10 cm?

• 1 < x < 5

• 7 < x < 13

• 8 < x 18

• not enough information

Answer explanation

difference of two side lengths < x < sum of two side lengths

A speaker in the shape of a cube with an edge length of 3.5 inches. The speaker is sold in a package in the shape of a square prism with a base area of 16 square inches and a height of 4.25 inches.

How much empty space, in cubic inches, remains in the package after the speaker is placed in the package?

Answer explanation

Find the volume of each shape.

The cube has a length of 3.5, meaning all sides of the cube are 3.5.

The square prism gives you the area of the base, so multiply by the height.

Then, subtract your two answers.

Tags

CCSS.7.G.B.6

A speaker in the shape of a cube with an edge length of 3.5 inches. The speaker is sold in a package in the shape of a square prism with a base area of 16 square inches and a height of 4.25 inches.

What is the surface area, in square inches of the package?

Answer explanation

You can use the net (by drawing one out) and finding the area of each shape. We knew the square base has an area of 16, so that means the length and width of the prism are both 4. They tell us the height is 4.25.

l x w x 2

l x h x 2

w x h x 2

4x4x2 = 32

4x4.25x2 = 34

4x4.25x2 = 34

Add all of your areas together to get 100.

Tags

CCSS.7.G.B.6