Week 10

Question 1

The concentric circles shown have radii of 1, 2, 3, and 4. Express the area of the shaded region in terms of π.

Answer 1

1. Find area of outer shaded area
2. Find area of inner shaded area
3. Add areas

7π + 3π = 10π

Question 2

What is the area of the shaded region if AO=8, ∠ABC=45∘ and O is the center of the circle?

Answer 2

1. Break region into right triangle and quarter circle.
2. Calculate area of right triangle and area of quarter circle
3. Add.

32+16π

Question 3

In this circle, A is the center of a circle with radius 4, and BC is an arc, or portion of the circumference.

Find the length of the arc.

Answer 3

1. Multiply the circumfrence by the fraction of the circle that the arc subtends

45/360 = 1/8

1/8 * 2*4*π= π

Question 4

Find the measure of arc AB.

Answer 4

Find DAB (50 degrees)

Double, finding arc DOB (100 degrees)

360-(150+100)=250

Question 5

Circles with centers A and B have radii 3 and 8, respectively. A common internal tangent intersects the circles at C and D, respectively. Lines AB and CD intersect at E, and AE=5. What is CD?

Note: A tangent is internal if the two circles lie on opposite sides of the line and are both tangent to it.

Answer 5

AEC (3,4,5 triangle) is similair to DEB

CE(4)+ED(10 2/3)=14 2/3

Question 6

The height of a right circular cylinder (commonly known as just a “cylinder”) is 3 times its radius. If its total surface area is 72π square units, then what is its volume?

Answer 6

2πr^2+2πr∗h is surface area formula.

Solve for r and h.

Calculate area (81π).

Question 7

A rectangular box has edges of length 9cm, 12cm, and 20cm. How long is the longest diagonal of the box?

Answer 7

Triangle HCB is a 3,4,5 right triangle with scaling factor 3,making HB 15.

Triangle HBA is a 3,4,5 right triangle with scaling factor 5,making HA 25.

Question 8

The surface area of the cube shown is 216. What is the area of triangle ACI?

Answer 8

Solve for length of edge (6).

Use side length (6√2) to find area of triangle