Perimeter, Area, and Surface Area — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Which formula finds how much paint is needed to cover the outside of a closed box?
A) SA = 2lw + 2lh + 2wh
B) V = l x w x h
C) P = 2(l+w)
D) A = 1/2 x b x h
Surface area sums all six faces, which is exactly what paint must cover on a closed box.
2. Which formula tells how much water fills a fish tank?
A) SA = 2lw + 2lh + 2wh
B) V = l x w x h
C) A = l x w
D) P = 4 x s
Volume V = l x w x h measures the cubic space inside the tank, which water fills.
3. A storage box is 8 m x 5 m x 4 m. What is its volume?
A) 80 cubic m
B) 120 cubic m
C) 160 cubic m
D) 200 cubic m
V = 8 x 5 x 4 = 160 cubic meters for the rectangular prism.
4. A cube has side 6 ft. What is its surface area?
A) 36 sq ft
B) 144 sq ft
C) 180 sq ft
D) 216 sq ft
SA = 6 x (6 x 6) = 6 x 36 = 216 square feet for a cube with 6-ft sides.
Part B: Fill in the Blank
Write the correct answer on each line.
1. A rectangular prism 7 ft x 4 ft x 3 ft has volume 84 cubic ft.
V = 7 x 4 x 3 = 84 cubic feet using the prism volume formula.
2. A box 10 cm x 6 cm x 4 cm has surface area 248 sq cm.
SA = 2(60) + 2(40) + 2(24) = 120 + 80 + 48 = 248 square centimeters.
3. A cube of side 7 m has volume 343 cubic m.
V = 7 x 7 x 7 = 343 cubic meters since all sides are equal.
4. A swimming pool 12 m x 6 m x 2 m holds 144 cubic m of water.
V = 12 x 6 x 2 = 144 cubic meters of water when the pool is full.
5. A box 5 in x 5 in x 5 in has surface area 150 sq in.
SA = 6 x (5 x 5) = 6 x 25 = 150 square inches for the cube.