Calculate the cubic units. Count the cube units. Write it down. Calculate the volume and then the area.

Here are the calculations for the cubic units (volume) and square areas (surface area) for each problem.

: Calculate the cubic units.

• Count the cube units (from the top image of the prism):

  • The prism has dimensions: Length = 5 units, Width = 4 units, Height = 3 units.
  • Volume: $$V = \text{Length} \times \text{Width} \times \text{Height}$$ $$V = 5 \text{ units} \times 4 \text{ units} \times 3 \text{ units}$$ $$V = 60 \text{ cubic units}$$
  • Surface Area: $$SA = 2(\text{Length} \times \text{Width} + \text{Length} \times \text{Height} + \text{Width} \times \text{Height})$$ $$SA = 2(5 \times 4 + 5 \times 3 + 4 \times 3)$$ $$SA = 2(20 + 15 + 12)$$ $$SA = 2(47)$$ $$SA = 94 \text{ square units}$$

• Write it down.

  • For "4 cubic units x 5 cubic units x 3 cubic units": $$V = 4 \text{ units} \times 5 \text{ units} \times 3 \text{ units}$$ $$V = \boxed{\text{60 cubic units}}$$
  • For "2 x (5 x 4) + 2 x (3 x 4) + 2 x (5 x 3)": $$SA = 2(20) + 2(12) + 2(15)$$ $$SA = 40 + 24 + 30$$ $$SA = \boxed{\text{94 square units}}$$

.a: Calculate the volume and then the area.

• The prism has dimensions: Length = 4 units, Width = 3 units, Height = 3 units.
  • Volume: $$V = 4 \text{ units} \times 3 \text{ units} \times 3 \text{ units}$$ $$V = \boxed{\text{36 cubic units}}$$
  • Surface Area: $$SA = 2(4 \times 3 + 4 \times 3 + 3 \times 3)$$ $$SA = 2(12 + 12 + 9)$$ $$SA = 2(33)$$ $$SA = \boxed{\text{66 square units}}$$

.c:

• For 3 cubic units x 3 cubic units x 4 cubic units:
  • Volume: $$V = 3 \text{ units} \times 3 \text{ units} \times 4 \text{ units}$$ $$V = \boxed{\text{36 cubic units}}$$
  • Surface Area: $$SA = 2(3 \times 3 + 3 \times 4 + 3 \times 4)$$ $$SA = 2(9 + 12 + 12)$$ $$SA = 2(33)$$ $$SA = \boxed{\text{66 square units}}$$

.d:

• For 5 cubic units x 6 cubic units x 4 cubic units:
  • Volume: $$V = 5 \text{ units} \times 6 \text{ units} \times 4 \text{ units}$$ $$V = \boxed{\text{120 cubic units}}$$
  • Surface Area: $$SA = 2(5 \times 6 + 5 \times 4 + 6 \times 4)$$ $$SA = 2(30 + 20 + 24)$$ $$SA = 2(74)$$ $$SA = \boxed{\text{148 square units}}$$

.e:

• For 7 cubic units x 8 cubic units x 9 cubic units:
  • Volume: $$V = 7 \text{ units} \times 8 \text{ units} \times 9 \text{ units}$$ $$V = \boxed{\text{504 cubic units}}$$
  • Surface Area: $$SA = 2(7 \times 8 + 7 \times 9 + 8 \times 9)$$ $$SA = 2(56 + 63 + 72)$$ $$SA = 2(191)$$ $$SA = \boxed{\text{382 square units}}$$

.f:

• For 4 cubic units x 8 cubic units x 12 cubic units:
  • Volume: $$V = 4 \text{ units} \times 8 \text{ units} \times 12 \text{ units}$$ $$V = \boxed{\text{384 cubic units}}$$
  • Surface Area: $$SA = 2(4 \times 8 + 4 \times 12 + 8 \times 12)$$ $$SA = 2(32 + 48 + 96)$$ $$SA = 2(176)$$ $$SA = \boxed{\text{352 square units}}$$

Millimetre fun:

• What will the surface area in square units be of a rectangular prism with 6 cubic units by 4 cubic units by 3 units?
  • Dimensions: Length = 6 units, Width = 4 units, Height = 3 units.
  • Surface Area: $$SA = 2(6 \times 4 + 6 \times 3 + 4 \times 3)$$ $$SA = 2(24 + 18 + 12)$$ $$SA = 2(54)$$ $$SA = \boxed{\text{108 square units}}$$