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?
(A) 16
(B) 8
(C) 4
(D) 2
(E) 2
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?
(A) 12
(B) 36
(C) 36
- 12
(D) 36 - 9
(E) 36
- 9
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
1. If the cube's volume is 64, then each edge has a length of 4.
2. The largest circle or sphere that fits inside this cube has a diameter of 4.
3. The radius is half the diameter, so the radius is 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?
Answer is
(D) 36 - 9
1. The area of the square is 36.
2. The area of the entire circle is 36
.
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
The answer is typically in terms of
.
3) The average of 12 consecutive even integers is 981. What's the highest of these integers?
Answer is
(E) 992
1. There are 12 numbers, so draw 12 spaces.
2. The average is 981, which goes right in the middle.
3. The consecutive numbers are even, 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.
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