Question 1
A right circular cone has a radius of 7 inches and a height of 9 inches. What is its volume, in cubic inches?
- A.
21π
- B.
441π
- C.
147π
- D.
294π
Answer: C. 147π
V = (1/3)πr²h = (1/3)π(7)²(9) = 147π.
SAT · Math · Geometry and Trigonometry
Area and volume
Area and volume is part of Geometry and Trigonometry in the SAT 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 composite or shaded region area, cylinder volume and liquid level, cone, sphere or pyramid volume and rectangular prism surface area and diagonals.
Common traps: adding the removed part; using diameter as radius; double-counting an overlap.
Sample questions
Question 2
A solid metal block measures 10 cm by 5 cm by 4 cm and is made of metal with a density of 7.8 grams per cubic centimetre. What is the mass of the block, in grams?
- A.
156
- B.
200
- C.
390
- D.
1,560
Answer: D. 1,560
Volume = 10 × 5 × 4 = 200 cm³ and mass = 200 × 7.8 = 1,560 g, choice D. Choice B is the volume with no density applied, A multiplies density by the 20 cm² face area, and C multiplies it by the 50 cm² face area; neither is a volume.
- A.
Question 3
A kiln shelf is a rectangle measuring 20 centimetres by 12 centimetres, with a circular vent of radius 3 centimetres cut completely through it. What is the area of the remaining shelf, in square centimetres, to the nearest tenth?
- A.
211.7
- B.
221.2
- C.
230.6
- D.
240.0
Answer: A. 211.7
The area is 20 × 12 − π(3)² = 240 − 9π ≈ 211.7 (A). Choice B subtracts 6π, the circumference; C subtracts 3π, using πr; D ignores the vent and gives the full rectangle's area.
- A.
Question 4
A tiler covers a rectangular floor measuring 4.8 metres by 3.6 metres exactly with 192 identical square tiles, with no gaps and no cutting. What is the side length of one tile, in centimetres?
Enter your own answer.
Answer: 30
The floor area is 4.8 × 3.6 = 17.28 m², so each tile has area 17.28 ÷ 192 = 0.09 m². The side is √0.09 = 0.3 m = 30 cm. Answering 0.09 or 9 stops at the area, and 0.3 forgets to convert metres to centimetres.
Question 5
A brass bar is a rectangular prism whose cross-section is a square 4 centimeters on each side. The bar has a mass of 1,088 grams, and the density of brass is 8.5 grams per cubic centimeter. How long is the bar, in centimeters?
- A.
8
- B.
32
- C.
68
- D.
128
Answer: A. 8
Volume = mass ÷ density = 1,088 ÷ 8.5 = 128 cubic centimeters. The square cross-section has area 4² = 16, so the length is 128 ÷ 16 = 8 (A). 128 is the volume itself, 32 divides by 4 instead of 4², and 68 divides the mass by 16 without first using the density.
- A.
Find your real gaps
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