Surface Area of 3D Figures
Finding the total area of the outside of solid shapes
Surface Area of 3D Figures
Finding the total area of the outside of solid shapes
Math - Grade 6-8
- 1
A cube has side length 4 cm. Find its surface area.
Use the formula for a cube: surface area = 6s^2.
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. - 2
A rectangular prism has length 6 m, width 3 m, and height 2 m. Find its surface area.
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. - 3
A rectangular prism measures 8 in by 5 in by 2 in. Find its surface area.
Find the areas of the three different face pairs, then double their sum.
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. - 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.
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. - 5
A square pyramid has base side length 6 ft and slant height 5 ft. Find its surface area.
Find the base area first, then add the areas of the 4 triangular sides.
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. - 6
A cylinder has radius 3 cm and height 8 cm. Use 3.14 for pi. Find its surface area.
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. - 7
A cylinder has diameter 10 m and height 7 m. Use 3.14 for pi. Find its surface area.
Remember that the radius is half the diameter.
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. - 8
A rectangular prism has length 9 cm, width 4 cm, and height 3 cm. Find its surface area.
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. - 9
A cube-shaped gift box has a surface area of 216 square inches. What is the side length of the box?
Start with 6s^2 = 216.
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. - 10
A square pyramid has base side length 10 cm and slant height 12 cm. Find its surface area.
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. - 11
A prism has a square base with side length 5 m and height 9 m. Find its surface area.
A square prism is a rectangular prism with a square base. Add the two bases and the four side rectangles.
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. - 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.
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. - 13
A cylinder has radius 4 ft and height 6 ft. Use 3.14 for pi. Find its surface area.
Surface area of a cylinder includes two circles and one curved surface.
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. - 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.
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. - 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.
When cubes are joined, the touching faces are inside the solid and are not part of the surface.
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.