AMC12 Geometry 3

Question 1

What is the area of a regular hexagon with side length 2?

Accepted Answer

6sqrt(3)

Answer

Area=(3sqrt(3)/2)*s^2=(3sqrt(3)/2)(4)=6sqrt(3).

Question 2

A sphere has surface area 100pi. What is its volume?

Accepted Answer

500pi/3

Answer

4pi*r^2=100pi gives r=5; V=(4/3)pi(125)=500pi/3.

Question 3

In a right triangle with legs 5 and 12, what is the altitude drawn from the right angle to the hypotenuse?

Accepted Answer

60/13

Answer

The hypotenuse is 13, and altitude=(5*12)/13=60/13.

Question 4

An external point is 5 units from the center of a circle with radius 3. What is the tangent segment length?

Accepted Answer

4

Answer

Tangent length=sqrt(d^2-r^2)=sqrt(25-9)=4.

Question 5

The diagonals of a parallelogram are 10 and 14 and intersect at right angles. What is the perimeter?

Accepted Answer

4sqrt(74)

Answer

Each side=sqrt(5^2+7^2)=sqrt(74), so perimeter=4sqrt(74).

AMC12 - American Mathematics Competition 12 Practice Test