Measurement and modeling

What is the formula for calculating the volume of a cube?

• V = l × w × h

Answer explanation

The volume of a cube is calculated using the formula V = a^3, where 'a' is the length of one side. This means you multiply the side length by itself three times, which is why this is the correct choice.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

If a cube has a side length of 3 cm, what is its volume?

• 9 cm³

• 18 cm³

• 27 cm³

• 36 cm³

Answer explanation

The volume of a cube is calculated using the formula V = side³. For a cube with a side length of 3 cm, V = 3³ = 27 cm³. Therefore, the correct answer is 27 cm³.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

Which formula is used to calculate the volume of a rectangular prism?

• V = l × w × h

Answer explanation

The volume of a rectangular prism is calculated using the formula V = l × w × h, where l is length, w is width, and h is height. This formula accurately represents the three-dimensional space occupied by the prism.

Tags

CCSS.7.G.B.6

What is the formula for the volume of a cylinder?

Answer explanation

The volume of a cylinder is calculated using the formula \(\pi r^2 h\), where \(r\) is the radius and \(h\) is the height. This formula accounts for the circular base area multiplied by the height.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How is the volume of a cone calculated?

Answer explanation

The volume of a cone is calculated using the formula \(\frac{1}{3} \pi r^2 h\), where \(r\) is the radius of the base and \(h\) is the height. This formula accounts for the cone's tapering shape.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the formula for the volume of a sphere?

Answer explanation

The volume of a sphere is calculated using the formula \(\frac{4}{3} \pi r^3\). This formula accounts for the three-dimensional space occupied by the sphere, where \(r\) is the radius.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How do you calculate the volume of a cylinder?

• \(2 \pi r h\)

Answer explanation

The volume of a cylinder is calculated using the formula \(\pi r^2 h\), where \(r\) is the radius and \(h\) is the height. This formula accounts for the circular base area multiplied by the height.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

• Cube

• Sphere

• Cone

• Cylinder

Answer explanation

The volume of a cone is calculated using the formula \(\frac{1}{3} \pi r^2 h\), where \(r\) is the radius of the base and \(h\) is the height. This distinguishes it from the other shapes listed.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What do you need to know to calculate the volume of a sphere?

• Height only

• Radius only

• Diameter only

• Length and width

Answer explanation

To calculate the volume of a sphere, you only need the radius. The formula is V = (4/3)πr³, where r is the radius. The other options, such as height or diameter, are not necessary for this calculation.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

The volume of a rectangular box is calculated by which formula?

• \(l \times w\)

• \(l \times w \times h\)

Answer explanation

The volume of a rectangular box is calculated using the formula \(l \times w \times h\), where \(l\) is length, \(w\) is width, and \(h\) is height. This formula accounts for all three dimensions of the box.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2