SAT Math Practice Question #770 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #770

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

A solid glass right circular cone has a height of \( H \) centimeters. A horizontal cut parallel to the base separates the solid cone into a smaller top cone and a bottom frustum. The volume of the bottom frustum is exactly \( \frac{117}{125} \) of the total volume of the original solid cone. If the height of the smaller top cone is \( 12 \text{ cm} \), what is the height of the frustum, in centimeters?
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Socratic AI Engine Step-by-Step Derivation
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Tactical Insight (Hint 1)

Break down the given equation or algebraic constraints step-by-step. Isolate the target variable before substituting known quantities.

Elimination Framework (Hint 2)

Elimination Shortcut: Check the extremes or test answer choices starting with C to binary search the correct magnitude.

Masterclass Solution & Distractor Trap Analysis

This geometry question separates the 750s from the 800s by testing the critical 3D scaling laws of similar figures, rather than just plugging numbers into volume formulas. Step 1: Understand the volume ratio of the cones. The problem gives ...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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