MP4 Geometry 9 weeks final review

What is the volume, in cubic meters, of a right rectangular prism that has a length of 2 meters, a width of 3 meters, and a height of 5 meters? Enter the number only, units are give.

Find the volume of the hexagonal prism pictured.

• 3132 m³

• 1806 m³

• 2264.56 m³
• 3365 m³

If the radius is 6 m, find the area of the shaded sectors. (Use the π button on your calculator).

Enter your response below: (Round your answer to the nearest tenths.)

A point in the figure is chosen at random. Find the probability that the point lies in the green shaded region.

• 25%

• 10%

• 50%

• 66%

Beau bought an automatic water bottle feeder for his hamster. A diagram of the bottle is shown. If h = 8, what is the maximum amount of water that the bottle can hold? Round your answer to the nearest hundredth.

Elijah has 5 shorts and 9 different polos to choose from. How many outfits are possible if he chooses 1 short and 1 polo?

• 40
• 50
• 45
• 30

You roll a six-sided die. What is the theoretical probability of rolling a multiple of 3?

• 1/2
• 1/4
• 1/3
• 2/3

You are asked to arrange the following 6 shaped in a line. There are special conditions you need to follow. The first is that the triangles and quadrilaterals must alternate, and the first shape must be a triable. How many 6-shape arrangements, with no repetitions, satisfy these conditions?

Answer explanation

Your pattern must be:

• Position 1: triangle

• Position 2: quadrilateral

• Position 3: triangle

• Position 4: quadrilateral

• Position 5: triangle

• Position 6: quadrilateral

So you're arranging:

• 3 distinct triangles into the 3 triangle positions

• 3 distinct quadrilaterals into the 3 quadrilateral positions

This is permutations without repetition, but within position categories.

• Number of ways to arrange 3 distinct triangles in 3 triangle spots = 3!3!3!

• Number of ways to arrange 3 distinct quadrilaterals in 3 quad spots = 3!3!3!

So total number of valid arrangements =

3!×3!=6×6=36​

A cube has a surface area of 24 square meters. What is the volume

• 12 cubic meters
• 6 cubic meters
• 4 cubic meters
• 8 cubic meters

There are 20 students on the mathletes club. How many ways can the club send 4 students to the next mathlete competition?