Practice Math Questions
Try these on for size.
1. What's the radius of the largest sphere that can be placed inside a cube of volume 64?
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2. One side of this square is on the radius of the circle. The circle's radius is 6. What's the area of the blue region?
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3. The average of 12 consecutive even integers is 981. What's the highest of these integers?
- (A) 988
- (B) 989
- (C) 990
- (D) 991
- (E) 992
Answers
1. What's the radius of the largest sphere that can be placed inside a cube of volume 64?
- Answer is (E) 2
How to solve:
- 1. If the cube's volume is 64, then each side is 4 wide.
- 2. The largest circle or sphere that would fit inside this cube would have a diameter of 4.
- 3. The radius is half the diameter, so its radius would be 2.
2. One side of this square is on the center of the circle. The circle's radius is 6. What's the area of the blue region?
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How to solve:
- 1. The area of the square is 36.
- 2. The area of the entire circle is 36
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- 3. Only 1/4 of the circle is in the drawing. 1/4 of 36 is 9.
- 4. Subtract the area of the quarter circle from the area of square.
- 5. The area of the blue region is 36 - 9
- Answers will almost always be in terms of .
3. The average of 12 consecutive even integers is 981. What's the highest of these integers?
- Answer is (E) 992
How to solve:
- 1. There are 12 numbers, so we'll draw 12 spaces.
- 2. The average is 981, so it goes right in the middle.
- 3. The numbers are consecutive even numbers, so we know what the next number is.
- 4. And from there, we know what all the other numbers are.
- 5. The highest is 992.