Section D Section D Checkpoint

Problem 1

Two candles are shaped like cylinders.

Candle A has a diameter of 8 cm and a height of 12 cm. Candle B has a radius of 5 cm and a height of 8 cm.

Which candle takes more wax to make? Explain or show your reasoning.

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Solution

Candle B. Sample reasoning: Candle A has a volume of about 602.88 cm3, since V=π⋅42 ⋅12≈603V=\pi \boldcdot 4^2 \boldcdot 12 \approx 603, while Candle B has a volume of about 628 cm3, since V=π⋅52 ⋅8≈628V=\pi \boldcdot 5^2 \boldcdot 8 \approx 628.

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Sample Response

Candle B. Sample reasoning: Candle A has a volume of about 602.88 cm3, since V=π⋅42 ⋅12≈603V=\pi \boldcdot 4^2 \boldcdot 12 \approx 603, while Candle B has a volume of about 628 cm3, since V=π⋅52 ⋅8≈628V=\pi \boldcdot 5^2 \boldcdot 8 \approx 628.

Problem 2

A cone has a height of 6 cm and a volume of 8π8 \pi cm3.

  1. Sketch the cone.
  2. Find its radius in centimeters. Explain or show your reasoning.
  3. Label your sketch with the cone’s height and radius.
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Solution
  1. See image.
  2. 2 cm. Sample reasoning: The volume of a cone is V=13πr2hV=\frac13 \pi r^2 h, so 8π=13πr2⋅68\pi=\frac13 \pi r^2 \boldcdot 6. This means 8=2r28=2r^2, so 4=r24=r^2, and r=2r=2.

  3. A cone with height 6 centimeters and radius 2 centimeters.
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Sample Response
  1. See image.
  2. 2 cm. Sample reasoning: The volume of a cone is V=13πr2hV=\frac13 \pi r^2 h, so 8π=13πr2⋅68\pi=\frac13 \pi r^2 \boldcdot 6. This means 8=2r28=2r^2, so 4=r24=r^2, and r=2r=2.

  3. A cone with height 6 centimeters and radius 2 centimeters.