Surface Area of 3D Figures Worksheet

Question 1

A cube has side length 4 cm. Find its surface area.

Accepted Answer

The surface area is 96 square centimeters. A cube has 6 equal faces, and each face has area 4 x 4 = 16 square centimeters, so 6 x 16 = 96 square centimeters.

Question 2

A rectangular prism has length 6 m, width 3 m, and height 2 m. Find its surface area.

Accepted Answer

The surface area is 72 square meters. Use 2(lw + lh + wh) = 2(6 x 3 + 6 x 2 + 3 x 2) = 2(18 + 12 + 6) = 72 square meters.

Question 3

A rectangular prism measures 8 in by 5 in by 2 in. Find its surface area.

Accepted Answer

The surface area is 132 square inches. Use 2(lw + lh + wh) = 2(8 x 5 + 8 x 2 + 5 x 2) = 2(40 + 16 + 10) = 132 square inches.

Question 4

A triangular prism has bases that are right triangles with side lengths 3 cm, 4 cm, and 5 cm. The length of the prism is 10 cm. Find its surface area.

Accepted Answer

The surface area is 132 square centimeters. The two triangular bases have total area 2 x (1/2 x 3 x 4) = 12 square centimeters. The lateral area is the perimeter of the triangle times the prism length, which is (3 + 4 + 5) x 10 = 120 square centimeters. Then 120 + 12 = 132 square centimeters.

Question 5

A square pyramid has base side length 6 ft and slant height 5 ft. Find its surface area.

Accepted Answer

The surface area is 96 square feet. The base area is 6 x 6 = 36 square feet. Each triangular face has area 1/2 x 6 x 5 = 15 square feet, and there are 4 faces, so the lateral area is 60 square feet. Then 36 + 60 = 96 square feet.

Question 6

A cylinder has radius 3 cm and height 8 cm. Use 3.14 for pi. Find its surface area.

Accepted Answer

The surface area is 207.24 square centimeters. Use 2pi r^2 + 2pi rh = 2 x 3.14 x 3^2 + 2 x 3.14 x 3 x 8 = 56.52 + 150.72 = 207.24 square centimeters.

Question 7

A cylinder has diameter 10 m and height 7 m. Use 3.14 for pi. Find its surface area.

Accepted Answer

The surface area is 376.8 square meters. The radius is 5 meters. Use 2pi r^2 + 2pi rh = 2 x 3.14 x 5^2 + 2 x 3.14 x 5 x 7 = 157 + 219.8 = 376.8 square meters.

Question 8

A rectangular prism has length 9 cm, width 4 cm, and height 3 cm. Find its surface area.

Accepted Answer

The surface area is 150 square centimeters. Use 2(lw + lh + wh) = 2(9 x 4 + 9 x 3 + 4 x 3) = 2(36 + 27 + 12) = 150 square centimeters.

Question 9

A cube-shaped gift box has a surface area of 216 square inches. What is the side length of the box?

Accepted Answer

The side length is 6 inches. For a cube, surface area = 6s^2, so 216 = 6s^2. Divide by 6 to get s^2 = 36, and then take the square root to get s = 6.

Question 10

A square pyramid has base side length 10 cm and slant height 12 cm. Find its surface area.

Accepted Answer

The surface area is 340 square centimeters. The base area is 10 x 10 = 100 square centimeters. Each triangular face has area 1/2 x 10 x 12 = 60 square centimeters, and there are 4 faces, so the lateral area is 240 square centimeters. Then 100 + 240 = 340 square centimeters.

Question 11

A prism has a square base with side length 5 m and height 9 m. Find its surface area.

Accepted Answer

The surface area is 205 square meters. The two square bases have total area 2 x 25 = 50 square meters. The lateral area is perimeter of base times height, which is (4 x 5) x 9 = 180 square meters. Then 50 + 180 = 230 square meters.

Question 12

A triangular prism has triangular bases with base 8 in and height 5 in. The other two sides of the triangle are 6 in and 7 in. The prism length is 12 in. Find its surface area.

Accepted Answer

The surface area is 220 square inches. One triangular base has area 1/2 x 8 x 5 = 20 square inches, so both bases have area 40 square inches. The perimeter of the triangle is 8 + 6 + 7 = 21 inches, so the lateral area is 21 x 12 = 252 square inches. Then 40 + 252 = 292 square inches.

Question 13

A cylinder has radius 4 ft and height 6 ft. Use 3.14 for pi. Find its surface area.

Accepted Answer

The surface area is 251.2 square feet. Use 2pi r^2 + 2pi rh = 2 x 3.14 x 4^2 + 2 x 3.14 x 4 x 6 = 100.48 + 150.72 = 251.2 square feet.

Question 14

A rectangular prism has surface area 94 square centimeters. Its length is 5 cm, width is 3 cm, and height is unknown. Find the height.

Accepted Answer

The height is 4 centimeters. Use 2(lw + lh + wh) = 94. Substitute the known values: 2(5 x 3 + 5h + 3h) = 94, so 2(15 + 8h) = 94. This gives 30 + 16h = 94, so 16h = 64 and h = 4.

Question 15

A composite solid is made of two identical cubes with side length 3 cm stacked face-to-face. Find the surface area of the solid.

Accepted Answer

The surface area is 54 square centimeters. Two cubes together form a rectangular prism with dimensions 3 cm by 3 cm by 6 cm. Its surface area is 2(lw + lh + wh) = 2(3 x 3 + 3 x 6 + 3 x 6) = 2(9 + 18 + 18) = 90 square centimeters.

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