Practice a variety of math problems to keep your math skills at their best. This week, fine-tune your geometry skills by working on the problems below!

### Points A and C lie on a circle with center R. The circle has a radius of 18 centimeters. The measure of

### ∠ARC is 90°. What is the length, in centimeters, of minor arc AC?

** **A) 36π

B) 26π

C) 14π

D) 9π

E) Cannot be determined

### Can you find the total circumference of the circle based on the information given?

A) 36π

B) 104π

C) 56π

D) 144π

E) No, not based on the information given

Stay tuned next week for the solution!

This question addresses volumes. **Step 1 is to find the volumes of the two vessels. **

The rectangle: V = length x width x height

V = 3 x 3.5 x 2

V = 21 feet

Convert feet to inches: V = 252 cubic inches

The cone cup: V = 1/3 π r^{2}

V = 1/3 π 2^{2}

**V = 20.94 cubic inches**

**Step 2 is to see how many cups of liquid are needed to fill the container to the max:**

Volume of box ÷ Volume of Cone

252 ÷ 20.94

12.0344

Analysis: If a contestant only pours 12 cups of liquid into the container, the container will not be completely full, especially if they spill any of the liquid. Instead, the contestant needs to go back for that 13^{th} cup of liquid in order to officially fill the container as, after the 12^{th} cup, there are still .0344 cubic inches of the container that needs liquid!