STAAR Category 3 Grade 8 Mathematics TEKS 8.6A/8.6B/8.7A. Student Activity 1
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1 Student Activity 1 Work with your partner to answer the following problems. Problem 1: The bases of a cylinder are two congruent that are to each other. The perpendicular distance between the two bases is called the of the cylinder. Problem 2: Find the volume of a cylinder with a diameter of 14 inches and a height of 4 inches. What is the of a cylinder? Diameter is inches. Height is inches. Draw and label a sketch of the cylinder. The diameter of the cylinder is inches so the radius of the cylinder is inches. Estimate: The area of the base is. Rounding it to and using 3 for, an estimate for the volume is cubic inches. The diameter of the cylinder is inches so the radius of the cylinder is inches. The formula for the volume of the cylinder is V =. Substitute for r and for h in the formula. Show your work. Justify: Evaluate: Problem 3: Find the volume of a cylinder with a circumference of 6 inches and a height that is twice the radius of the cylinder. What is the of a cylinder? Circumference is inches. Height is inches. Draw and label a sketch of the cylinder. TEKSING TOWARD STAAR 2014 Page 1
2 Find the diameter from the circumference: The diameter of the cylinder is inches so the radius of the cylinder is inches. Estimate: The area of the base is. Rounding it to and using 3 for, an estimate for the volume is cubic inches. The formula for the volume of the cylinder is V =. Substitute for r and for h in the formula. Show your work. Justify: Evaluate: Problem 4: Compare the volumes of the two cylinders described below. Cylinder A: Radius: 6 inches Height: 12 inches Cylinder B: Radius: 12 inches Height: 6 inches Problem 5: What change will happen to the volume of a cylinder if the height is doubled? What change will happen to the volume of a cylinder if the radius is doubled? TEKSING TOWARD STAAR 2014 Page 2
3 Student Activity 2 Work with your partner to answer the following problems. Problem 1: Find the volume of a cone with a radius of 10 inches and a height of 12 inches. Problem 2: A cylinder and a cone have the same base and height. The volume of the cone is approximately 56 cubic feet. What is the volume of the cylinder? Problem 3: A waffle cone has a radius of 3 inches and a height of 5 inches. What is the volume of the cone? TEKSING TOWARD STAAR 2014 Page 3
4 Student Activity 3 Work with your partner to answer the following problems. Problem 1: A cylinder has a volume of 36 cubic units. It has a radius of 2 units. What is the height of the cylinder? What is the height of the cylinder? The volume is cubic units. The radius is units. Use the volume of a formula. Find the area of the circular base using the area of a circle formula. Substitute the values for volume and base area. Solve the equation for h. V Bh B = ( ) 2 36 h 9 = h (divided both sides by ) The volume of a cylinder with a radius of 2 and a height of 9 is 2 (2) 9. This agrees with the given volume so our solution of h = is reasonable. Problem 2: A cone has a diameter of 8 inches and a volume of 24 cubic inches. What is the height of the cone? Problem 3: A cone has a radius that is 12 inches and a height of 24 inches. 24 inches 12 inches What is the volume of the cone to the nearest square inch? TEKSING TOWARD STAAR 2014 Page 4
5 Problem 4: A glass jar of jelly is shaped like a cylinder. The jar has a height of 8 inches and a base with a diameter of 4 inches. There are 5 inches of grape jelly left in the jar as shown below. 8 in. 5 in. 4 in. What is the volume of the jelly in the jar? How much of the jelly has the family eaten if we assume the jar was completely full when purchased? TEKSING TOWARD STAAR 2014 Page 5
6 NAME DATE SCORE /5 8.6A/8.6B/8.7A Skills and Concepts Homework 1 1. A cylinder has a radius of 9 centimeters and a height of 20 centimeters. Find the area of the base of the cylinder. Show your work. Find the volume of the cylinder. Show your work. 2. A cylinder is filled with 1 centimeter cubes. The bottom of the cylinder is shown below. What is the area of the squares (top of the cubes) shown above? If the cubes are stacked 8 in each stack, how many cubes are in the cylinder? What is the volume of the cubes? If the diameter of the cylinder is 5.5 centimeters and the height is 8 centimeters, what is the volume of the cylinder? What is the difference between the volume of the cylinder and the volume of the cubes? 3. Find the volume of a cylinder that has a diameter of 20 centimeters and a height of 9 centimeters. Show your work. Find the volume of a cone with the same dimensions as the cylinder above. What is the ratio of the volume of the cylinder to the volume of the cone? TEKSING TOWARD STAAR 2014 Page 6
7 4. A cylinder has a base circumference of 24 inches and a height of 12 inches. What is the volume of the cylinder? What is the volume of a cone with the same dimensions as the cylinder? 5. A student states that a cylinder with a 6-inch radius will have a volume twice the volume of a cylinder with the same height but a 3-inch radius. Is he correct? If not, determine the relationship of the two volumes. TEKSING TOWARD STAAR 2014 Page 7
8 NAME DATE SCORE /5 8.6A/8.6B/8.7A Skills and Concepts Homework 2 1. What is the volume of the cylinder represented below? Show your work. 10 cm 14 cm 2. A cylinder has a volume of 245 cubic units. Its height is 5 units. What is the radius of the cylinder? Show your work. 3. A cone has a volume of 1,024 cubic units. Its radius is 16 units. What is the height of the cone? Show your work. 4. The diameter of a cone is 6 inches and a height of 8 inches. How much greater is the volume of a cylinder with the same diameter and same height? Show your work. 5. The road construction on Broad Street in Mansfield has about 90 orange cones in various spots. Each cone is about 30 inches tall and has a diameter of 18 inches. What is the volume of the 90 cones? Show your work. TEKSING TOWARD STAAR 2014 Page 8
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