TEKS 8.7D Worksheets — Grade 8 Determine the volume of cylinders, cones, and

During a field trip to Palo Duro Canyon, Maya and her classmates are designing a new lookout platform in the shape of a cylinder. The platform will have a radius of 3 feet and a height of 5 feet. How many cubic feet of space will the platform occupy?

1. 45π ✓
2. 27π
3. 15π
4. 60π

Why: To find the volume of a cylinder, you can use the formula V = πr²h, where r is the radius and h is the height. In this case, the radius is 3 feet and the height is 5 feet. First, calculate the area of the base: r² = 3² = 9 square feet. Then multiply by the height: 9 × 5 = 45 cubic feet. Therefore, the volume of the cylinder is 45π cubic feet.

Marquise is designing a cylindrical rainwater collection barrel for his garden in Texas. The barrel has a radius of 3 feet and a height of 4 feet. He needs to know how much water it can hold in cubic feet. What is the volume of the barrel? Use 3.14 for pi.

1. 113.04 ✓
2. 37.68
3. 94.20
4. 75.36

Why: To find the volume V of a cylinder, you use the formula V = πr^2h, where r is the radius and h is the height. Here, r = 3 feet and h = 4 feet. Plugging in the numbers: V = 3.14 * (3^2) * 4 = 3.14 * 9 * 4 = 113.04 cubic feet. Thus, the correct answer is 113.04.

Mei is designing a water fountain shaped like a cone for a park in Austin, Texas. The fountain has a radius of 3 feet and a height of 5 feet. To find out how much water the fountain can hold, she wants to calculate its volume. Use the formula for the volume of a cone, V = (1/3) * pi * r^2 * h. What is the volume of the fountain in cubic feet (use 3.14 for pi)?

1. 47.1 ✓
2. 15.7
3. 94.2
4. 39.3

Why: To find the volume of the cone, use the formula V = (1/3) * pi * r^2 * h. Plugging in the values, we have V = (1/3) * 3.14 * (3^2) * 5. First, calculate the area of the base: 3^2 = 9. Then, V = (1/3) * 3.14 * 9 * 5 = (1/3) * 3.14 * 45. This equals 141.3 / 3 = 47.1. Therefore, the volume of the fountain is 47.1 cubic feet.

Khalil is designing a water fountain in his backyard in Austin, Texas, that will be shaped like a cone. The fountain will have a base radius of 3 feet and a height of 5 feet. What is the volume of the fountain? Use 3.14 for pi.

1. 47.1 cubic feet ✓
2. 15.7 cubic feet
3. 9.42 cubic feet
4. 94.2 cubic feet

Why: To find the volume of a cone, use the formula V = (1/3) * pi * r^2 * h. First, calculate the base area: r^2 = 3^2 = 9. Then, 9 * 3.14 = 28.26. Now, multiply by the height: 28.26 * 5 = 141.3. Finally, divide by 3: 141.3 / 3 = 47.1. The volume of the fountain is 47.1 cubic feet.

Paola is planning to make a giant piñata shaped like a cone for her school fundraiser in San Antonio. The piñata will have a base radius of 3 feet and a height of 7 feet. Which expression can be used to calculate the volume of the piñata in cubic feet?

1. (1/3) * π * (3^2) * 7 ✓
2. (1/3) * π * 3 * 7^2
3. (1/3) * π * (7^2) * 3
4. (1/2) * π * (3^2) * 7

Why: The correct expression to calculate the volume of a cone is (1/3) * π * r^2 * h, where r is the radius and h is the height. In this case, the radius is 3 feet and the height is 7 feet, so the volume can be expressed as (1/3) * π * (3^2) * 7.

Mason is designing a water tank for his family's farm in Lubbock, Texas. The tank has the shape of a cylinder with a radius of 4 feet and a height of 10 feet. What is the volume of the tank in cubic feet? Use 3.14 for π.

1. 502.4 ✓
2. 160
3. 125.6
4. 80

Why: To find the volume of the cylinder, use the formula V = πr²h. Plugging in the values, V = 3.14 * (4²) * 10 = 3.14 * 16 * 10 = 502.4 cubic feet. Therefore, the correct answer is 502.4.

Caroline wants to create a large drink dispenser for her lemonade stand at the San Antonio River Walk. The dispenser is designed in the shape of a cylinder with a radius of 10 inches and a height of 12 inches. What is the volume of the drink dispenser in cubic inches? Use 3.14 for pi in your calculations.

1. 376.8
2. 1200
3. 3768 ✓
4. 1200.48

Why: To find the volume of the cylindrical drink dispenser, we use the formula for the volume of a cylinder: V = pi * r^2 * h. Here, the radius (r) is 10 inches and the height (h) is 12 inches. Substituting the values, we calculate V = 3.14 * (10^2) * 12 = 3.14 * 100 * 12 = 3.14 * 1200 = 3768 cubic inches. Therefore, the correct answer is 3768.

Amelia is designing a cylindrical water tank for her family’s fishery in Galveston. The tank has a radius of 5 feet and a height of 10 feet. What is the volume of the tank in cubic feet?

1. 785 cubic feet ✓
2. 1570 cubic feet
3. 125 cubic feet
4. 314 cubic feet

Why: To find the volume of a cylinder, use the formula V = πr²h, where r is the radius and h is the height. Here, the radius is 5 feet and the height is 10 feet. First, calculate r²: 5 * 5 = 25. Then, multiply this by the height: 25 * 10 = 250. Finally, multiply by π (approximately 3.14): 250 * 3.14 = 785 cubic feet. Therefore, the correct answer is 785 cubic feet.