Digital SAT Math Practice Question #1175
Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.
How do you calculate the volume of a rectangular prism and the volume of a cylinder?
Carefully read the description of how the hole is drilled. Which dimension of the block corresponds to the length (or height) of the cylindrical hole?
⚡ Hack the Test: While direct calculation is straightforward here, a quick sanity check can help. The volume of the block is 480. The volume of the hole is \(40\pi\). Since \(\pi \approx 3.14\), \(40\pi \approx 40 \times 3.14 = 125.6\). So the remaining volume is approximately \(480 - 125.6 = 354.4\). Look at the options: A: \(480 - 24\pi \approx 480 - 75.36 = 404.64\) B: \(480 - 40\pi \approx 480 - 125.6 = 354.4\) C: \(480 - 16\pi \approx 480 - 50.24 = 429.76\) D: \(480 - 8\pi \approx 480 - 25.12 = 454.88\) All options are numerically distinct enough that a rough estimation of \(\pi\) (e.g., 3 or 3.1) would quickly confirm option B as the only plausible answer if you had made a minor calculation error in the \(\pi\) term. The key is correctly identifying the cylinder's length.
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