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Name Class Date

1. A candle maker has a block of paraffin that is 4 centimeters high by 8 centimeters long by 6 centimeters wide. He melts it into a cone-shaped candle that is 5 centimeters wide at the base and 25 centimeters tall. Does the candle maker use all of the paraffin from the original block? How do you know?

2. An inflatable spherical exercise ball and an inflatable cylindrical ottoman both have a diameter of 24 inches. Both hold the same amount of air. What is the height of the ottoman? Use 3.14 for π. Justify your answer.

3. A potter makes a cylindrical vase that is 14 inches high and 8 inches wide. The base and sides of the vase are 0.25 inch thick.

a. How tall and wide is the hollow cylindrical interior of this vase? Explain your reasoning.

b. What is the volume of the interior? Use 3.14 for π. Round your answer to the nearest cubic inch.

Performance Task

MCC8.G.9

UNIT 3

Unit 3 165 Performance Task

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c. Another vase having the same outside dimensions has thicker sides. Choose a side thickness and calculate the volume. Is the inside volume of this vase greater or less than the volume of the original vase?

4. A company makes snow globes. Each snow globe is in the shape of a sphere, and the diameter of the sphere is 8 centimeters.

a. One cubic centimeter of water has a mass of about 1 gram. If the snow globe is filled with water, what is the total mass of the water in the snow globe? Explain how you found your answer. Use 3.14 for π and round to the nearest whole gram.

b. The company has another snow globe with a diameter of 9 centimeters and a mass of 934 grams. The plastic shell, decorations, and base make up 454 grams of that mass. Is the snow globe filled with water? Explain your reasoning.

Unit 3 166 Performance Task