Geometry End of Unit 4 Summative Study Guide

A right rectangular prism has a length of 10 inches, a width of 8 inches, and a height of 6 inches. What is the surface area in square inches? ________ square inches

• 480 square inches

• 376 square inches

• 188 square inches

• 240 square inches

Answer explanation

The surface area of a right rectangular prism is calculated using the formula: 2(lw + lh + wh). Substituting the values: 2(10*8 + 10*6 + 8*6) = 2(80 + 60 + 48) = 2(188) = 376 square inches. Thus, the correct answer is 376 square inches.

Tags

CCSS.7.G.B.6

Brody wraps a cube-shaped present. One side of the present measures 2.4 ft. How much wrapping paper will Brody need to cover the present?

• 2.4 square feet

• 5.76 square feet

• 13.82 square feet

• 34.56 square feet

Answer explanation

To find the surface area of a cube, use the formula 6a², where a is the length of a side. Here, a = 2.4 ft. So, 6 * (2.4)² = 6 * 5.76 = 34.56 square feet. Thus, Brody needs 34.56 square feet of wrapping paper.

Tags

CCSS.6.G.A.4

What is the surface area of the right triangular prism shown?

• 576 square cm

• 288 square cm

• 336 square cm

• 168 square cm

Answer explanation

To find the surface area of a right triangular prism, calculate the area of the triangular base and the three rectangular faces. The correct total surface area is 336 square cm.

Tags

CCSS.7.G.B.6

Hermione made a jewelry box shaped like the rectangular prism below. What is the surface area of the jewelry box?

• 351 cm²

• 366 cm²

• 183 cm²

• 25 cm²

Answer explanation

To find the surface area of a rectangular prism, use the formula: 2(lw + lh + wh). If the dimensions are given, substituting them will yield 366 cm², confirming that this is the correct answer.

Tags

CCSS.7.G.B.6

The city paints a cylindrical water tower with a radius of 6 meters and a height of 10 meters. What is the approximate surface area that is painted?

• 226.08 m²

• 376.8 m²

• 602.88 m²

• 1130.4 m²

Answer explanation

To find the surface area of a cylindrical water tower, use the formula: Surface Area = 2πr(h + r). Here, r = 6m and h = 10m. Calculating gives approximately 602.88 m², which is the correct answer.

If a cylinder is sliced parallel to its base, what will be the shape of the cross section?

• circle

• square

• rectangle

• ellipse

Answer explanation

When a cylinder is sliced parallel to its base, the cross section is a circle. This is because all points on the circular base are equidistant from the center, maintaining the circular shape in the cross section.

Tags

CCSS.7.G.A.3

Which of the following can be a cross section of a cube?

• square

• triangle

• hexagon

• circle

Answer explanation

A cube can be sliced in various ways. A square is the most common cross section, but a triangle and hexagon can also result from specific cuts. A circle cannot be a cross section of a cube.

Tags

CCSS.7.G.A.3

The cross section of a figure is the same whether it is cut horizontally or vertically. What could the figure be?

• triangular prism

• sphere

• cylinder

• none of the above

Answer explanation

The sphere has the same cross section regardless of whether it is cut horizontally or vertically, resulting in a circle. In contrast, a triangular prism and a cylinder have different cross sections depending on the cut direction.

Tags

CCSS.7.G.A.3

A cylinder is sliced parallel to the base. What shape is created by the cross section?

• circle

• rectangle

• ellipse

• cone

Answer explanation

When a cylinder is sliced parallel to its base, the cross section is a circle. This is because all points on the cross section are equidistant from the center, maintaining the circular shape of the base.

Tags

CCSS.7.G.A.3

A block of wood is in the shape of a right rectangular pyramid, as shown. If the block is cut parallel to the base, which of the following describes the cross-section?

• a square

• a triangle

• a rectangle that is not a square

• a parallelogram that is not a rectangle

Answer explanation

When a right rectangular pyramid is cut parallel to its base, the cross-section formed is a rectangle. Since the base is rectangular and the cut is parallel, the resulting shape is a rectangle that is not a square.

Tags

CCSS.7.G.A.3