IB Test Circles Practice

Helen is building a cabin using cylindrical logs of length 2.4 m and radius 8.4 cm. A wedge is cut from one log and the cross-section of this log is illustrated in the diagram.

Find the volume of this log.

Hint: The radius is in centimeters and the height of the cylinder is in meters, so you have to do a units conversion.

Your answer is between 45000 and 46000. Don't leave it in terms of pi, this program won't recognize it. Use a calculator and get a decimal, round to three sig figs.

Mathematical Equivalence

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Answer explanation

Listen to the clue I uploaded here.

The diagram shows points in a park viewed from above, at a specific moment in time. A is a tree in the park. Odette is standing at point O, Khemil is standing at point K, and the football they are playing with is at point X. XY is a semicircular path with center A such that angle KAY is 45 degrees.

Khemil runs along the semicircular path to pick up the football. Calculate the distance Khemil runs.

Hint: Khemil is running from K to X on the round part, so figure out the number of degrees he runs first. Then find the arc length. Your answer is between 28 and 29.

Mathematical Equivalence

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Answer explanation

A landscaping firm proposes a design for a new park. A fence in the shape of a circular arc with center A is to be installed connecting B, E, and D. This is illustrated in the diagram. Angle BAD is 77 degrees.

Find the perimeter of the proposed park ABED.

Hint: You will need to find the arc length of the arc connecting BED and then add the two side lengths. Your answer is between 280 and 290. Don't leave it in terms of pi.

Mathematical Equivalence

ON

Answer explanation

The straight metal arm of a windscreen wiper on a car rotates in a circular motion from a pivot point O through an angle of 140 degrees. The windscreen is cleared by a rubber blade of length 46 cm that is attached to the metal arm between points A and B. The total length of the metal arm, OB, is 56 cm. The part of the windscreen cleared by the rubber blade is shown unshaded in the diagram.

Calculate the length of this arc made by B, the end of the rubber blade.

Hint: Your answer should be between 130 and 140. Make sure not to keep it in terms of pi.

Mathematical Equivalence

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Answer explanation

The diagram shows a sector, OAB, of a circle with centre O and radius r, such that AOB=θ. Sam measured the value of r to be 2 cm and the value of θ to be 30 degrees.

Use Sam’s measurements to calculate the area of the sector. Give your answer to four significant figures.

Hint: Your answer is between 1 and 2.

Mathematical Equivalence

ON

Answer explanation