Answer:
1. The surface area of the cube is 324 square units
The volume of the cube 360 unit cube
2. The surface area of the cylinder is approximately 169.65 square units
The volume of the cylinder is approximately 169.65 unit cube
3. The surface area of a square pyramid is 360 square units
The volume of the square pyramid is 400 unit cube
4. The surface area of a cone is approximately 452.39 square units
The volume of the cone is approximately 50.27 unit cube
5. The surface area of the triangular prism is 240 square units
The volume of the triangular prism is 180 unit cube
6. The surface area of the sphere is approximately 804.25 square units
The volume of the sphere is approximately 2.144.66
7. The surface area of the composite figure is approximately 653.46 square units
The volume of the composite figure is approximately 1,474.45 unit cube
Step-by-step explanation:
1. The surface area of the figure, SA = 2 × (w·h + l·w + h·l)
Where;
w = The width of the figure = 6
l = The length of the figure = 12
h = The height of the figure = 5
We get;
SA = 2 × (6 × 5 + 12 × 6 + 5 × 12) = 324
The surface area of the figure, SA = 324
The volume of the figure, V = l × w × h
∴ V = 12 × 6 × 5 = 360
The volume of the figure, V = 360
2. The surface area of a cylinder, SA = 2·π·r² + 2·π·r·h
The radius of the given cylinder, r = 3
The height of the given cylinder, h = 6
∴ SA = 2×π×3² + 2×π×3×6 ≈ 169.65
The surface area of the cylinder, SA ≈ 169.65
The volume of a cylinder, V = π·r²·h
∴ V = π×3²×6 ≈ 169.65
The volume of the cylinder, V ≈ 169.65
3. The surface area of a square pyramid, SA = b² + 4·(1/2)·b·√((b/2)² + h²)
Therefore, for the given square pyramid, we have;
SA = 10² + 4×(1/2)×10×√((10/2)² + 12²) = 360
The surface area of a square pyramid, SA = 360
The volume of a square pyramid, V = (1/3) × Area of Base × Height
Therefore, or the given pyramid we have;
V = (1/3) × 10² × 12 = 400
The volume of the square pyramid, V = 400
4. The surface area of a cone, SA = π·r·(r + l)
Where;
The radius of the cone = r
The slant height of the cone, l = 10
The height of the cone, h = 6
∴ The radius of the cone, r = √(10² - 6²) = 8
∴ SA = π×8×(8 + 10) ≈ 452.39
The surface area of a cone, SA ≈ 452.39
The volume of the cone, V = (1/3) × π·r·h
∴ V = (1/3) × π × 8 × 6 ≈ 50.27
The volume of the cone, V ≈ 50.27
5. The surface area of the triangular prism, SA = 2 × (1/2)× b·h + b·w + h·w + w·l
Where;
b = The base length of the triangular surfaces = 5
h = The height of the triangular surfaces = 12
w = The width of the triangular prism = 6
l = The slant length of the prism = 13
Therefore;
SA = 2 × (1/2)× 5 × 12 + 5 × 6 + 12 × 6 + 6 × 13 = 240
The surface area of the triangular prism, SA = 240
The volume of a triangular prism, V = (1/2)·b·h·w
V = (1/2) × 5 × 12 × 6 = 180
The volume of the triangular prism, V = 180
6. The surface of a sphere, SA = 4·π·r²
Where;
r = The radius of the sphere = 8
∴ SA = 4 × π × 8² ≈ 804.25
The surface area of the sphere, SA ≈ 804.25
The volume of a sphere, V = (4/3)·π·r³
∴ V ≈ (4/3)×π×8³ ≈ 2,144.66
The volume of the given sphere, V ≈ 2.144.66
7. The figure is a composite figure made up of a cone and an hemispher
The surface area of the cone shaped part of the figure, SA = π·r·l
Where;
r = The radius of the cone = 8
l = The slant height of the cone = 10
∴ SA₁ = π × 8 × 10 ≈ 251.34
The surface area of the cone shaped part of the figure, SA₁ ≈ 251.34
The volume of the cone, V₁ = (1/3)·π·r²·h
Where;
h = The height of the cone = √(10² - 8²) = 6
∴ V₁ = (1/3) × π × 8² × 6 ≈ 402.12
The volume of the cone, V₁ ≈ 402.12
The surface area of the hemisphere, SA₂ = 2·π·r²
∴ SA₂ = 2 × π × 8² ≈ 402.12
The surface area of the hemisphere, SA₂ ≈ 402.12
The volume of a hemisphere, V₂ = (2/3)·π·r³
∴ V₂ = (2/3) × π × 8³ ≈ 1072.33
The volume of a hemisphere, V₂ ≈ 1,072.33
The surface area of the composite figure, SA = SA₁ + SA₂
∴ SA = 251.34 + 402.12 = 653.46
The surface area of the composite figure, SA ≈ 653.46
The volume of the composite figure, V = V₁ + V₂
∴ V = 402.12 + 1,072.33 = 1,474.45
The volume of the composite figure, V ≈ 1,474.45.
