Surface area unit test unit 6 lesson 12

Answer 1

1. Calculate the surface area of a rectangular prism with dimensions 5 cm x 3 cm x 7 cm.

- Surface Area = 2lw + 2lh + 2wh
- Surface Area = 2(5)(3) + 2(5)(7) + 2(3)(7)
- Surface Area = 30 + 70 + 42
- Surface Area = 142 cm²

2. Find the surface area of a cube with a side length of 4 cm.

- Surface Area = 6s²
- Surface Area = 6(4)²
- Surface Area = 6(16)
- Surface Area = 96 cm²

3. A cylindrical can has a radius of 2 inches and a height of 8 inches. Calculate the total surface area of the can.

- Surface Area = 2πr² + 2πrh
- Surface Area = 2π(2)² + 2π(2)(8)
- Surface Area = 2π(4) + 2π(16)
- Surface Area = 8π + 32π
- Surface Area = 40π
- Surface Area ≈ 125.6 in²

4. A triangular prism has a base with a height of 6 inches and a base with dimensions of 4 inches by 5 inches. Calculate the total surface area of the prism.

- Surface Area = 2B + Ph
- Surface Area = 2(0.5bh) + P(6)
- Surface Area = 2(0.5)(4)(5) + (4 + 5 + √(4² + 6²))(6)
- Surface Area = 2(10) + (9 + √52)(6)
- Surface Area = 20 + (9 + 7.2)(6)
- Surface Area = 20 + (16.2)(6)
- Surface Area = 20 + 97.2
- Surface Area = 117.2 in²

5. Calculate the surface area of a sphere with a radius of 3 cm.

- Surface Area = 4πr²
- Surface Area = 4π(3)²
- Surface Area = 4π(9)
- Surface Area = 36π
- Surface Area ≈ 113.04 cm²

6. Find the surface area of a cone with a radius of 5 cm and a slant height of 8 cm.

- Surface Area = πr² + πrl
- Surface Area = π(5)² + π(5)(8)
- Surface Area = π(25) + π(40)
- Surface Area = 25π + 40π
- Surface Area = 65π
- Surface Area ≈ 204.2 cm²

7. A pyramid has a square base with sides of 6 cm and a height of 9 cm. Calculate the total surface area of the pyramid.

- Surface Area = B + 0.5Pl
- Surface Area = 6² + 0.5(4)(6 + √(3² + 4.5²))(9)
- Surface Area = 36 + 12(6 + √(9 + 20.25))(9)
- Surface Area = 36 + 72(6 + √(29.25))(9)
- Surface Area = 36 + (432 + 648√29.25)
- Surface Area = 36 + 432 + 648(5.4)
- Surface Area = 36 + 432 + 3499.2
- Surface Area = 468 + 3499.2
- Surface Area ≈ 3967.2 cm²

8. Calculate the surface area of a rectangular pyramid with base dimensions of 8 cm by 5 cm and a height of 10 cm.

- Surface Area = B + 0.5Pl
- Surface Area = 8(5) + 0.5(4)(8 + 5 + √(4² + 5²))(10)
- Surface Area = 40 + 0.5(7)(18 + √41)(10)
- Surface Area = 40 + 3.5(180 + 18√41)
- Surface Area = 40 + 630 + 63√41
- Surface Area = 670 + 63√41
- Surface Area ≈ 747.17 cm²

These are some examples of calculations for finding the surface area of different geometric shapes.