ACT · Math · Integrating Essential Skills

Area, perimeter, and volume

Area, perimeter, and volume is part of Integrating Essential Skills in the ACT Math section. The questions below are written in the style of the real test, each with the answer and a worked explanation.

Question types you will see here include perimeter and fencing problems, area of a composite figure, volume of a prism or cylinder, volume of a cone, sphere and or pyramid.

Common traps: including the open side; using area instead of perimeter; forgetting to multiply by the cost per unit.

Sample questions

Question 1
A right circular cone has a radius of 3 inches and a height of 4 inches. What is its volume, in cubic inches?
- A.
  12π
- B.
  4π
- C.
  36π
- D.
  24π
Answer: A. 12π
V = (1/3)πr²h = (1/3)π(3)²(4) = 12π.
Question 2
A running track in Sharjah has two straight sections of 100 m each, joined at the ends by two semicircles, each with a diameter of 60 m. To the nearest meter, what is the distance around the track?
- A.
  260
- B.
  389
- C.
  577
- D.
  8,828
Answer: B. 389
The two semicircles form one circle of circumference π(60) ≈ 188.5, plus 200 for the straights = 388.5 ≈ 389 m. Choice A (260) treats the curved ends as 60 m straight pieces. Choice C (577) counts the curved ends as two full circles. Choice D (8,828) computes area instead of distance.
Question 3
A cylindrical grain silo has a diameter of 6 meters and a height of 10 meters. To the nearest cubic meter, what is its volume?
- A.
  28
- B.
  94
- C.
  188
- D.
  283
Answer: D. 283
The radius is 3 m, so V = πr²h = π(9)(10) ≈ 282.7, or 283 cubic meters. Choice A (28) is the area of the base only; Choice B (94) uses πrh; Choice C (188) uses the lateral surface area.
Question 4
A gym in Pune fences a rectangular courtyard that measures 20 m by 15 m. Fence goes along both 15 m sides and one 20 m side; the other 20 m side is the building wall. Fence costs ₹38 per meter. What is the total cost of the fence?
- A.
  ₹1,900
- B.
  ₹2,090
- C.
  ₹2,660
- D.
  ₹11,400
Answer: A. ₹1,900
The fence is 20 + 15 + 15 = 50 m, and 50 × 38 = ₹1,900. B fences both 20 m sides and only one 15 m side. C fences all four sides, 70 m. D multiplies the area, 300 m², by the price per meter.
Question 5
A rectangular roof in Chennai measures 9 m by 6 m. A gutter is installed along both 9 m edges and one 6 m edge to carry rainwater into a tank. The gutter costs 150 rupees per meter. What is the total cost of the gutter, in rupees?
- A.
  2,700
- B.
  3,150
- C.
  3,600
- D.
  4,500
Answer: C. 3,600
The gutter runs 9 + 9 + 6 = 24 m, costing 24 × 150 = 3,600 rupees. Only three edges are included. Choice A (2,700) counts only the two 9 m edges. Choice B (3,150) counts only one of the 9 m edges and both 6 m edges. Choice D (4,500) gutters all four edges.

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