Illustrative Mathematics - Geometry - Unit 5 - Lesson 17

The washer in the image has an inner diameter of \frac{1}{4} inch. The outer diameter measures \frac{3}{4} inch, and the washer is \frac{1}{4} inch thick. The density of the metal the washers are made of is 0.285 pounds per cubic inch. How much do 5 washers weigh, in pounds? Round your answer to the nearest hundredth.

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The density of water is 1 gram per cm3. An object floats in water if its density is less than water’s density, and it sinks if its density is greater than water’s. Will a toy in the shape of a rectangular prism that is 1 centimeter by 2 centimeter by 2 centimeter with mass 3 grams sink or float? Explain your reasoning.

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A cube and a sphere both have volume 512 cubic units. Which solid has a greater surface area? Explain your reasoning.

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A pyramid has a height of 4 inches and a volume of 40 cubic inches. Select all figures that could be the base for this pyramid.

• a 5 inch by 2 inch rectangle
• a 3 inch by 10 inch rectangle
• a triangle with height 10 inches and base 3 inches
• a right triangle with one side 5 inches and the hypotenuse 13 inches
• a heart with area 30 square inches

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Select all solids for which the formula V=Bh applies.

• a triangular prism
• a triangular pyramid
• a square pyramid
• a rectangular prism
• a cone

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Two distinct lines, l and m, are each perpendicular to the same line n. A fourth distinct line, k, is also perpendicular to line n. Does line k intersect line l or line ? Explain how you know.

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