Understanding Spheres in Proportion

This video tutorial covers the concept of spheres in proportion, focusing on the relationships between linear measurements, surface area, and volume. It explains how to calculate these properties using ratios and provides examples to illustrate these concepts. The tutorial also includes practical exercises to apply the learned concepts, helping students understand the proportional relationships in spheres.

What is the first measurement needed to understand the proportions of a sphere?

• Surface area

• Volume

• Circumference

• Radius or diameter

If the radius of a sphere is tripled, how does the surface area change?

• It remains the same

• It becomes 6 times larger

• It becomes 3 times larger

• It becomes 9 times larger

For a sphere with a radius ratio of 2:5, what is the ratio of their surface areas?

• 4:25

• 2:5

• 1:3

• 8:125

If the volume ratio of two spheres is 1:8, what is the ratio of their radii?

• 1:5

• 1:3

• 1:4

• 1:2

What happens to the volume of a sphere if its radius is doubled?

• It remains the same

• It becomes 8 times larger

• It becomes 4 times larger

• It becomes 2 times larger

If a sphere's radius is halved, how does its surface area change?

• It becomes 4 times smaller

• It remains the same

• It becomes 2 times smaller

• It becomes 8 times smaller

When the radius of a sphere is quadrupled, what is the change in its volume?

• It remains the same

• It becomes 32 times larger

• It becomes 64 times larger

• It becomes 16 times larger

If the radius of a sphere is reduced to one-third, what happens to its volume?

• It remains the same

• It becomes 1/3 of the original

• It becomes 1/27 of the original

• It becomes 1/9 of the original

What is the relationship between the radius and surface area of a sphere?

• Surface area is inversely proportional to the radius

• Surface area is proportional to the cube of the radius

• Surface area is proportional to the square of the radius

• Surface area is directly proportional to the radius

If the radius of a sphere is increased by a factor of 4, how does the surface area change?

• It remains the same

• It becomes 4 times larger

• It becomes 8 times larger

• It becomes 16 times larger