Volume and Surface Area of Solids

This video tutorial covers the volume of a sphere, comparing it with cones and cylinders. It explains how to sketch a sphere and calculate its volume using formulas. The tutorial also includes practice problems and examples to reinforce understanding of volume calculations for spheres, cones, and cylinders.

What is the first step in sketching a sphere?

• Draw a rectangle

• Draw a square

• Draw a circle

• Draw a triangle

If the radius of a cylinder is 5 units, what is the diameter?

• 5 units

• 10 units

• 15 units

• 20 units

What fraction of a cylinder's volume is the volume of a cone with the same radius and height?

• 1/3

• 1/4

• 1/2

• 2/3

How do the volumes of a cone and a sphere compare to the volume of a cylinder with the same radius and height?

• The sphere alone fills the cylinder

• The cone alone fills the cylinder

• The cone and sphere together fill the cylinder

• Neither fills the cylinder

What is the formula for the volume of a sphere?

• V = 4/3πr³

• V = πr²h

• V = 2/3πr³

• V = 1/3πr²h

If a sphere fits snugly inside a cube with an edge length of 8, what is the radius of the sphere?

• 2

• 4

• 6

• 8

What fraction of the cube's volume is occupied by the sphere inside it?

• 1/2

• 1/3

• 1/4

• 1/6

If the radius of sphere B is double that of sphere A, how many times greater is the volume of sphere B compared to sphere A?

• 8 times

• 6 times

• 2 times

• 4 times

In a bicycle shop, if the number of bicycles is two fewer than ten times the number of tricycles, and there are 410 wheels in total, how many bicycles are there?

• 178

• 180

• 182

• 184

What is the volume of a sphere with a radius of 4?

• 512π/3

• 256π/3

• 64π/3

• 128π/3