AIME Geometry 3

Question 1

A sphere has radius 3. Find its volume in terms of π.

Accepted Answer

36π

Answer

27π

Answer

12π

Answer

108π

Question 2

In a 30-60-90 triangle, the hypotenuse is 10. Find the length of the shorter leg.

Accepted Answer

5

Answer

10

Answer

5√3

Answer

5√2

Question 3

What is the area of a trapezoid with parallel bases 6 and 10 and height 4?

Accepted Answer

32

Answer

24

Answer

40

Answer

16

Question 4

Chord AB and chord CD intersect inside a circle. If AX=3, XB=8, CX=4, find XD.

Accepted Answer

6

Answer

8

Answer

12

Answer

4

Question 5

A cylinder has radius 5 and height 8. What is its total surface area?

Accepted Answer

130π

Answer

80π

Answer

100π

Answer

160π

Question 6

In triangle ABC with sides a=7, b=24, c=25, what type of triangle is it?

Accepted Answer

Right

Answer

Acute

Answer

Obtuse

Answer

Equilateral