Exploring Volumes of 3D Shapes

• Area of Base

• Radius of Base

• Diameter of Base

• Base height

Answer explanation

In the formula for the volume of a cone, the letter B represents the Area of the Base. The volume is calculated using the formula V = (1/3)Bh, where B is the area of the circular base and h is the height of the cone.

• Area of Base

• Radius of Base

• Diameter of Base

• Base height

Answer explanation

In the formula for the volume of a cylinder, the letter B represents the Area of the Base. The volume is calculated as V = B * h, where B is the area of the circular base and h is the height of the cylinder.

• Area of Base

• Radius of Base

• Diameter of Base

• Not applicable or not found

Answer explanation

In the formula for the volume of a cylinder, $V = B h$, $B$ represents the area of the base. The base is a circle, so $B = \pi r^2$ is correct.

Answer explanation

In the formula for the volume of a cone, $V = \frac{1}{3} B h$, $B$ represents the area of the base. The base of a cone is a circle, so $B = \pi r^2$ is correct.

• No Area of Base (B)

Answer explanation

In the context of the volume of a sphere, there is no area of base (B) as the formula is derived from the volume formula \( V = \frac{4}{3} \pi r^3 \). Thus, the correct choice is 'No Area of Base (B)'.

What is the formula for the volume of a cylinder?

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 multiplied by the height, making it the correct choice.

What is the formula for the volume of a cone?

Answer explanation

The volume of a cone is calculated using the formula V=\frac{1}{3}\pi r^2h, 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.

What is the formula for the volume of a sphere?

Answer explanation

The volume of a sphere is given by 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, unlike the other options which are for different shapes.

If the diameter of a cone is 10 cm, what is the radius?

• 5 cm

• 10 cm

• 15 cm

• 20 cm

Answer explanation

The radius of a cone is half of its diameter. Given the diameter is 10 cm, the radius is 10 cm ÷ 2 = 5 cm. Therefore, the correct answer is 5 cm.