By the end of this lesson, you should be able to:

Directions:

The answers are printed in white, and by highlighting the space after (and beneath) the word, Answer, these answers become visible.

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1. Which is longer, a line that passes through (2,3) and (2,4) or a line that passes through (2,3) and (5,3)?

Answer => Neither, they are both infinitely long and extend beyond the points indicated because they are lines, not line segments.

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2. Which is larger, the perimeter of a square plot of land that measures 100 meters on a side, or the circumference of a circular plot of land that has a diameter of 120 meters?

Answer => The square's perimeter is 400 meters, which is larger than the circle's circumference of 377 meters.

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3. A typical picture frame has four 90^o angles. Each piece of the frame is cut with a miter cut at a 45^o angle to produce the typical picture frame corner. What angle would I use for the miter cut if I wanted to make a pentagonal frame with equal sides and angles?

Answer => 54^o: The sum of the interior angles is (n - 2) * 180^o or 540^o, giving each internal angle a measurement of 108^o.

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4. What is the area of the isosceles triangle to the right if its two legs measure 13m and 17m?

Answer => 102.1 square meters

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5. CoolTreats sells an ice cream cone (sugar cone) that has an inside diameter of 2 inches and an inside altitude of 4 inches. They want to know the diameter of a spherical scoop of ice cream that will melt to exactly fill the cone (assuming no change in volume when melting.) Find the diameter of that sphere.

Answer => 2 inches

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6. There are two pulleys connected with a belt. The larger pulley has a radius of 8 inches, and the smaller has a radius of 2 inches. If the smaller pulley rotates at 100 revolutions per minute, determine the revolutions per minute of the larger pulley.

Answer => 25 rpm.