Volume and Surface Area Concepts

The video tutorial explains how to calculate the volume of a sphere using the formula V = 4/3 π r³. It provides examples of calculating volume with a given radius and converting diameter to radius. The tutorial also covers finding the radius from a given volume and calculating the volume of a hemisphere and a silo. The process involves using mathematical operations and rounding results to the nearest tenth or thousand as required.

What is the formula for the volume of a sphere?

• V = 2/3 π r³

• V = 4/3 π r²

• V = π r² h

• V = 4/3 π r³

When calculating the volume of a sphere, which dimension is primarily needed?

• Radius

• Diameter

• Height

• Circumference

In the formula V = 4/3 π r³, what does 'r' represent?

• Diameter of the sphere

• Radius of the sphere

• Circumference of the sphere

• Height of the sphere

If the radius of a sphere is 4 cm, what is the exact volume in terms of π?

• 512/3 π cm³

• 128/3 π cm³

• 256/3 π cm³

• 64/3 π cm³

How do you round 268.08 to the nearest tenth?

• 268.1

• 268.0

• 268.2

• 268.3

What is the first step when given the diameter of a sphere to find its volume?

• Multiply the diameter by π

• Convert the diameter to radius

• Use the diameter directly in the formula

• Square the diameter

If the diameter of a sphere is 10 feet, what is the radius?

• 10 feet

• 20 feet

• 5 feet

• 15 feet

What is the exact volume of a sphere with a radius of 5 feet in terms of π?

• 125/3 π feet³

• 1000/3 π feet³

• 250/3 π feet³

• 500/3 π feet³

How do you find the radius of a sphere if the volume is given as 288π?

• Use the formula V = 4/3 π r³ and solve for r

• Multiply the volume by 4/3 and solve for r

• Divide the volume by π and solve for r

• Subtract π from the volume and solve for r

What is the cube root of 216?

• 7

• 6

• 8

• 5