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How do you find the volume of a cylinder?

• V= ^1/₃ πr²h

• V= ^4/₃ πr²h

• V= ^4/₃ πr³

• V= πr²h

Answer explanation

The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height. This formula accounts for the circular base area (πr²) multiplied by the height (h).

Tags

CCSS.7.G.B.6

How do you find the volume of a cone?

• V= ^1/₃ πr²h

• V= ^4/₃ πr²h

• V= ^4/₃ πr³

• V= πr²h

Answer explanation

The volume of a cone is calculated using the formula V = (1/3)πr²h, where r is the radius of the base and h is the height. This formula accounts for the cone's tapering shape, making the correct choice V = (1/3)πr²h.

Tags

CCSS.7.G.B.6

How do you find the volume of a sphere?

• V= ^1/₃ πr²h

• V= ^4/₃ πr²h

• V= ^4/₃ πr³

• V= πr²h

Answer explanation

The volume of a sphere is calculated using the formula V = \frac{4}{3} \pi r^3, where r is the radius. This formula accounts for the three-dimensional nature of a sphere, making it the correct choice.

Tags

CCSS.7.G.B.6

Which figure has a volume of 45π ft³?

• Cylinder with a height of 5ft and diameter of 6 ft

• Sphere with a radius of 3 ft

• Cone with a radius of 3 feet and height of 5 ft

• Sphere with a diameter of 5 feet

Answer explanation

The volume of a cylinder is calculated using the formula V = πr²h. For the cylinder with a height of 5 ft and diameter of 6 ft (radius 3 ft), V = π(3²)(5) = 45π ft³, confirming it as the correct choice.

Tags

CCSS.7.G.B.6

The figure shown below is composed of a rectangular prism and two half cylinders. Which is closest to the volume of the figure?

• 781 cm³

• 706 cm³

• 631 cm³

• 593 cm³

Answer explanation

To find the volume, calculate the volume of the rectangular prism and the two half cylinders. The total volume is approximately 706 cm³, making it the closest choice to the actual volume.

Tags

CCSS.7.G.B.6

A table tennis ball has a diameter of 40 mm. What is the approximate volume of the table tennis ball in cubic millimeters?

• 1,676 mm³

• 18,850 mm³

• 33,510.3 mm³

• 268,083 mm³

Answer explanation

To find the volume of a sphere, use the formula V = (4/3)πr³. The radius r is half the diameter, so r = 20 mm. Calculating gives V ≈ 33,510.3 mm³, which matches the correct answer.

Tags

CCSS.7.G.B.6

Russell is filling a cylinder-shaped swimming pool that has a diameter of 20 feet. He fills it with water to a depth of 3 feet. What is the volume of the water in the pool, to the nearest cubic foot?

• 377 cubic feet

• 942 cubic feet

• 2,958 cubic feet

• 3,768  cubic feet

Answer explanation

To find the volume of water, use the formula for the volume of a cylinder: V = πr²h. The radius r is 10 feet (half of the diameter), and the height h is 3 feet. Thus, V = π(10)²(3) ≈ 942 cubic feet, which is the correct answer.

Tags

CCSS.7.G.B.4

CCSS.7.G.B.6

How do you find the volume of a cylinder?

• V= ^1/₃ πr²h

• V= ^4/₃ πr²h

• V= ^4/₃ πr³

• V= πr²h

Answer explanation

The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height. This formula accounts for the circular base area (πr²) multiplied by the height (h).

Tags

CCSS.7.G.B.6

How do you find the volume of a cone?

• V= ^1/₃ πr²h

• V= ^4/₃ πr²h

• V= ^4/₃ πr³

• V= πr²h

Answer explanation

The volume of a cone is calculated using the formula V = (1/3)πr²h, where r is the radius of the base and h is the height. This formula accounts for the cone's tapering shape, distinguishing it from a cylinder.

Tags

CCSS.7.G.B.6

How do you find the volume of a sphere?

• V= ^1/₃ πr²h

• V= ^4/₃ πr²h

• V= ^4/₃ πr³

• V= πr²h

Answer explanation

The volume of a sphere is calculated using the formula V = \frac{4}{3} \pi r^3, where r is the radius. This formula accounts for the three-dimensional nature of a sphere, making it the correct choice.

Tags

CCSS.7.G.B.6