Name: Date: Period: Chapter 9: 3-D Figures Topic 3: Volume Day 2

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1 Name: Date: Period: Do Now: Chapter 9: 3-D Figures Topic 3: Volume Day 2 1.) A rectangular prism has a volume of 3x x Its base has a length of x + 2 and a width of 3. Which expression represents the height of the prism? (1) x + 4 (2) x + 2 (3) 3 (4) x 2 + 6x ) The Parkside Packing Company needs a rectangular shipping box. The box must have a length of 11 inches and a width of 8 inches. Find, to the nearest tenth of an inch, the minimum height of a box such that the volume is at least 800 cubic inches. More Challenging Volume Problems: 1.) A planned building was going to be 120 feet long, 70 feet deep, and 30 feet high. The owner decides to increase the volume of the building by 10% without changing the dimensions of the depth and height. What will be the new length of the building? 2.) A sphere is inscribed inside a cube with edges of 6 cm. In cubic centimeters, what is the volume of the sphere, in terms of pi.

2 3.) A sphere with a radius of 10 centimeters is in a cube-shaped box with a 20 centimeter edge. (a) Determine the volume of both the cube and the sphere. (b) What percentage, to the nearest tenth, does the ball fill? 4.) A cone fits inside a cylinder so that their bases are the same, as shown in the diagram below. Calculate the volume that is inside the cylinder but outside of the cone. Give an exact answer. The radius is 5 and the height is ) A cone sits inside a cube with a side length of 26 inches. Determine the volume, to the nearest tenth of an inch, that is inside the cube but outside of the cone.

3 6.) Preston is designing a mold for a concrete block to bus used in a custom landscaping project. The block is shown in the diagram with its corresponding dimensions and consists of two intersecting rectangular prisms. Find the volume, in cubic inches, needed to make Preston s custom block. Density: and are related. Density is described as the mass of the substance per volume. Formula: density = Examples: 1.) A square metal plate has a density of 10.2 g/cm 3 and weighs kg. (a) Calculate the volume of the plate. (hint: 1 kg = 1000 g) (b) If the bases of this plate has an area of 25 cm 2, determine its thickness.

4 2.) A metal cup full of water has a mass of 1,000 g. The cup itself has a mass of g. If the cup has both a diameter and a height of 10 cm, what is the approximate density of water? 3.) A box in the shape of a right rectangular prism has a length of 10 in, width 8 in, and height 15 in. When completely filled the box has a density of 0.05 pounds per cubic inch. (a) Determine its mass. (b) If a second box has linear dimensions twice those of the fist box, find the weight of the box when completely filled with contents of the same type.

5 Name: Date: Period: Volume Day 2: Homework Complete the questions below. Show all work, including formulas. 1.) The diagram shows a wooden block that has a hole drilled in it. The diameter of the hole is 2 cm. Calculate the volume of this solid. Round your answer to the nearest hundredth. 2.) The diagram shows the cross-section of a pipe that is 50 inches long. The inner diameter of the pipe is 20 inches and the other diameter is 30 inches. Calculate the volume of the metal needed to make the pipe. Round your answer to the nearest tenth. 3.) A planned building was going to be 100 feet long, 75 feet deep, and 30 feet high. The owner decides to increase the volume of the building by 10% without changing the dimensions of the depth and the height. What will be the new length of this building? (1) 106 ft (2) 110 ft (3) 108 ft (4) 112 ft 4.) Gold has a density of g/cm 3. If a square pyramid has a base edge length of 5 cm, a height of 6 cm, and a mass of 942 g, is the pyramid in fact solid gold?

6 5.) Cylinders X and Y are right cylinders with equal volumes. Cylinder X has a height of 4 feet and a radius of 1 foot. Cylinder Y has a height of 5 feet. What is the radius of cylinder Y, rounded to the nearest tenth of a foot. 6.) The right cylinder shown below has a height of 7.5 meters. A cone is contained within the cylinder. The cone and the cylinder share a base. The vertex, X, of the cone is located in the same plane as the top of the cylinder. The volume of the cone is 385 cubic meters. What is the radius of the cylinder to the nearest tenth of a meter? Review Questions: 7.) The figure below shows two areas formed by the wooden support of a swing. The lengths of several dimensions of the structure, in feet, are given. Angles B and E are congruent. How long, in feet, is the side represented by? DE (1) 5 (2) 2 (3) 3 (4) 6

7 8.) Consider ABC and GHI. GHI ABC. Which of the following statements is true? (1) AC HI (2) AB GH (3) BAC GHI (4) BCA GHI 9.) In the following image, line JK and line LM are parallel. Line NQ is a transversal that interects line LM at point O and line JK at point P. The m MOP = 3x + 2 and m JPO = 4x 13. What is the measure of JPN? 10.) Name the composite transformation that moved the original figure to the figure named as transformation 2.