Answer:
a) The volume of the prism is 660 mm³
b) The surface area of the prism is 514 mm²
Step-by-step explanation:
The given prism for which we are to find the volume and the surface area shows the dimensions of the sides
a) To find the volume, we can consider the prism as a composite figure as follows;
The topmost cuboid with dimensions (15 - 2×3) mm, 3 mm, and 9 mm
Therefore, the volume of the topmost cuboid, V₁, is given as follows;
V₁ = 5 mm × 3 mm × 9 mm = 135 mm³
The volume of the cuboid on which the top cuboid rest, V₂, is given as follows;
V₂ = 15 mm × 5 mm × 7 mm = 525 mm³
The volume of the prism, V = V₁ + V₂
Therefore, we have;
V =135 mm³ + 525 mm³ = 660 mm³
The volume of the prism, V = 660 mm³
b) The surface area of the prism is given as follows;
The surface area of the top cuboid, SA₁, is given as follows;
SA₁ = 9 mm × 5 mm + 2 × 3 mm × 9 mm + 2 × 3 mm × 5 mm = 129 mm²
The surface area of the larger cuboid, SA₂, is given as follows;
SA₂ = 2 × 15 mm × 7 mm + 2 × 5 mm × 7 mm + 2 × 3 mm × 5 mm + 15 mm × 5 mm = 385 mm²
The surface area of the prism, SA = SA₁ + SA₂
∴ The surface area of the prism, SA = 129 mm² + 385 mm² = 514 mm²
