Geometry Flashcards

6 cards from real AIME practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 Geometry flashcards as text

A sphere has radius 3. Find its volume in terms of π.
Answer: 36π
V=(4/3)πr^3=(4/3)π(27)=36π.
In a 30-60-90 triangle, the hypotenuse is 10. Find the length of the shorter leg.
Answer: 5
In a 30-60-90 triangle, the shorter leg is half the hypotenuse: 10/2=5.
What is the area of a trapezoid with parallel bases 6 and 10 and height 4?
Answer: 32
Area=(b₁+b₂)/2×h=(6+10)/2×4=32.
Chord AB and chord CD intersect inside a circle. If AX=3, XB=8, CX=4, find XD.
Answer: 6
By the intersecting chords theorem, AX·XB=CX·XD: 3×8=4×XD, so XD=6.
A cylinder has radius 5 and height 8. What is its total surface area?
Answer: 130π
Total SA=2πr^2+2πrh=2π(25)+2π(40)=50π+80π=130π.
In triangle ABC with sides a=7, b=24, c=25, what type of triangle is it?
Answer: Right
Check: 7^2+24^2=49+576=625=25^2, confirming it is a right triangle by the converse of the Pythagorean theorem.