Surface Area of Rectangular Prisms Worksheet

Question 1

A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Find its surface area.

Accepted Answer

The surface area is 158 square cm because 2(8 x 5) + 2(8 x 3) + 2(5 x 3) = 80 + 48 + 30 = 158.

Question 2

A cube has side lengths of 6 inches. Find the surface area of the cube.

Accepted Answer

The surface area is 216 square inches because each face has an area of 6 x 6 = 36 square inches, and 6 faces have a total area of 6 x 36 = 216 square inches.

Question 3

A cereal box is 20 cm tall, 12 cm wide, and 5 cm deep. How much cardboard is needed to make the outside of the box, not including any overlap?

Accepted Answer

The box needs 680 square cm of cardboard because 2(20 x 12) + 2(20 x 5) + 2(12 x 5) = 480 + 200 + 120 = 800 square cm.

Question 4

A rectangular prism has a length of 8 m and a height of 3 m. Its total surface area is 158 square m. What is its width?

Accepted Answer

The width is 5 m. Using SA = 2lw + 2lh + 2wh gives 158 = 2(8w) + 2(8 x 3) + 2(3w), so 158 = 16w + 48 + 6w. Then 110 = 22w, so w = 5.

Question 5

An open-top aquarium is 10 ft long, 6 ft wide, and 8 ft tall. It has glass on the bottom and four sides, but not on the top. How many square feet of glass are needed?

Accepted Answer

The aquarium needs 316 square feet of glass because the bottom is 10 x 6 = 60, the two long sides total 2(10 x 8) = 160, and the two short sides total 2(6 x 8) = 96. The total is 60 + 160 + 96 = 316.

Question 6

A net for a rectangular prism has two rectangles that are 4 cm by 3 cm, two rectangles that are 4 cm by 2 cm, and two rectangles that are 3 cm by 2 cm. What is the surface area of the prism?

Accepted Answer

The surface area is 52 square cm because 2(4 x 3) + 2(4 x 2) + 2(3 x 2) = 24 + 16 + 12 = 52.

Question 7

Box A measures 12 in by 4 in by 3 in. Box B measures 8 in by 6 in by 3 in. Which box has the greater surface area, and by how much?

Accepted Answer

Box A has the greater surface area by 12 square inches. Box A has surface area 2(12 x 4) + 2(12 x 3) + 2(4 x 3) = 192 square inches. Box B has surface area 2(8 x 6) + 2(8 x 3) + 2(6 x 3) = 180 square inches.

Question 8

A gift box is 15 cm long, 9 cm wide, and 4 cm high. You need enough wrapping paper to cover the box plus 20 extra square cm for overlap. How much wrapping paper is needed?

Accepted Answer

You need 482 square cm of wrapping paper. The surface area is 2(15 x 9) + 2(15 x 4) + 2(9 x 4) = 270 + 120 + 72 = 462 square cm, and 462 + 20 = 482 square cm.

Question 9

A student says the surface area of a rectangular prism with length 10 cm, width 6 cm, and height 4 cm is 40 square cm because 2(10 + 6 + 4) = 40. Explain the mistake and find the correct surface area.

Accepted Answer

The mistake is adding the side lengths instead of finding the areas of the faces. The correct surface area is 2(10 x 6) + 2(10 x 4) + 2(6 x 4) = 120 + 80 + 48 = 248 square cm.

Question 10

A small wooden block is shaped like a rectangular prism with dimensions 2 cm by 2 cm by 5 cm. If all outside faces are painted, what total area is painted?

Accepted Answer

The painted area is 48 square cm because 2(2 x 2) + 2(2 x 5) + 2(2 x 5) = 8 + 20 + 20 = 48.

Question 11

A rectangular storage bin is 2.5 m long, 1.2 m wide, and 0.8 m high. Find its surface area.

Accepted Answer

The surface area is 11.92 square m because 2(2.5 x 1.2) + 2(2.5 x 0.8) + 2(1.2 x 0.8) = 6 + 4 + 1.92 = 11.92.

Question 12

A rectangular prism has a square base. The base is 5 cm by 5 cm, and the prism is 12 cm tall. Find the surface area.

Accepted Answer

The surface area is 290 square cm. The top and bottom total 2(5 x 5) = 50 square cm, and the four side faces total 4(5 x 12) = 240 square cm, so the total is 290 square cm.

Question 13

A shipping label covers only the four side faces of a box, not the top or bottom. The box is 14 in long, 10 in wide, and 6 in high. What total area can the label cover?

Accepted Answer

The label can cover 288 square inches. The two long side faces total 2(14 x 6) = 168 square inches, and the two short side faces total 2(10 x 6) = 120 square inches. The total is 168 + 120 = 288.

Question 14

A rectangular prism is built from unit cubes and measures 4 cubes long, 3 cubes wide, and 2 cubes high. How many square unit faces are on the outside of the prism?

Accepted Answer

There are 52 square unit faces on the outside. The surface area is 2(4 x 3) + 2(4 x 2) + 2(3 x 2) = 24 + 16 + 12 = 52 square units.

Question 15

Two rectangular prisms both have a volume of 64 cubic cm. Prism A measures 8 cm by 4 cm by 2 cm. Prism B measures 4 cm by 4 cm by 4 cm. Which prism has the smaller surface area?

Accepted Answer

Prism B has the smaller surface area. Prism A has surface area 2(8 x 4) + 2(8 x 2) + 2(4 x 2) = 112 square cm. Prism B has surface area 6(4 x 4) = 96 square cm, which is smaller.

Surface Area of Rectangular Prisms

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