Circle and Square II

Which has the greater area: a 10-centimeter square, or a circle with a diameter of 11 centimeters? Explain your answer.

Circle and Square I

The diameter of a circle is the same length as the side of a square. How much greater is the area of the square?

A. It isn't greater; the circle and square have the same area.

B. The area of the square is 25% greater.

C. The area of the square is 27.3% greater.

D. The area of the square is 50% greater.

E. The area of the square is 54.6% greater.

Explain your answer.

More Odd Numbers

The sum of a sequence of odd numbers is always divisible by half of the sum of the first and last odd numbers in the sequence. For example, 7 + 9 + 11 + 13 is divisible by ½(7 + 13), and 3 + 5 + 7 + 9 + 11 is divisible by ½(3 + 11). Why?

Odd Numbers

It's been a hectic month. I am now employed again, and have had little time for word problems. However, here's a good brain teaser.

A number is "singly even" if it can be evenly divided by 2 but not by 4. The numbers 2, 6, 10, 14, 18, ... are all "singly even." Show that the sum of a sequential series of odd numbers (e. g., 9 + 11 + 13 + 15) must be odd or divisible by 4; it cannot be "singly even."

Stock Up

Walter buys shares of a stock for $1000 on Monday. On Tuesday, the stock gains 10%. On Wednesday it loses 10%. What is the value of the stock at the end of trading on Wednesday?

Twice and Thrice

The sum of two integers is twice their difference. Their product is three times their difference. What are the two integers?

Easy Does It

The ratio of two numbers is twice their sum, and their difference is zero. What are the two numbers?

Equilateral Perimeter

The perimeter of an equilateral triangle is twice the area. What is the length of a side?

Twin Triangles

Line CD is parallel to AB. What is the ratio of the area of ΔACE to ΔBDE? How do you know?

Quadrilateral Area 4

Use what you know of triangles to find the area of the quadrilateral shown above.

Quadrilateral Area 3

Use what you know of triangles to find the area of the quadrilateral shown above.

Quadrilateral Area 2

Find the area of the quadrilateral shown above.

Quadrilateral Area 1

Find the area of the quadrilateral shown above.

Maximum Apex

The base of a triangle is twice its height. What is the maximum measure of the angle opposite the base (the apex)?

Angle Ratio

The interior angles of a triangle have a ratio of 1:2:3. If the shortest side of this triangle is 2 cm, what is the length of the longest side?

Another Angle

The ratio of ∠ABC to ∠CDE is 4:5. What is the measure of ∠CBD?

Good Pi

A common approximation of π is ²²/₇ = 3.142857. Using 3.141593 as the value of π, compute the percent error introduced by using ²²/₇  instead.

Test Guessing

A ten-question test consists of true-or-false questions. What is the probability that a student who guesses at every answer will get them all wrong?

Volume Tolerance

Each side of a cube must measure 1.00 inches ± 1%. What will be the percent tolerance for the volume?

Great Pyramid

The Great Pyramid of Giza was 280 cubits tall when built. Each side of the base was 440 cubits. What was the volume in cubic cubits? Round your answer to two significant digits.

Coin Toss

You flip a fair coin three times in a row. What is the probability that the coin will land heads up at least twice?

Can Label

Belinda needs to design a label for a can. The can is 4³/₈" tall and 2⁷/₈" in diameter. The label requires ¹/₈" clearance for the rim at the top and bottom of the can. It must wrap around the can with at least ¹/₄" overlap for glue. To the nearest ¹/₁₆", what are the dimensions of the label Belinda must design?

Missing Segment

Line AB is parallel to line CD. Find the measure of segment AE using the information provided. Can you also find the length of segment BE?

Triangle Ratios

Line AB is parallel to line CD. The measure of segment AB is twice the measure of segment CD. What is the ratio between the area of ΔABE and ΔCDE?

Compare Areas

Line BD is parallel to line AC. What is the relationship of the area of triangle ABD to triangle BCD?

1. The areas are the same.
2. The area of ABD is greater than the area of BCD.
3. The area of ABD is less than the area of BCD.
4. Impossible to tell from given information.

Room Volume

A room is 15' long, 12' wide, and 8' high. What is the volume of the room in cubic feet?

Triangle Troubles

Find the value of y. Find the area of the triangle. Find the value of x. What is the measure of angle B (the top angle)?

Seventy-two

For each of the following three-digit numbers, insert one digit anywhere to make a number divisible by 72.

151, 352, 511, 722, 812, 993

Meet Vi Hart

For anyone who doubts that math can be fun, take a look at this site created by a young woman with a love for the beauty and weirdness of numbers. Here's a recent video she made.

Enjoy!