Volume and Height of 3D Shapes

This video tutorial covers various mathematical problems related to geometry and algebra. It begins with calculating the volume of spheres and matching them to descriptions. It then explores the volume of a cube and a sphere fitting inside it, followed by comparing volumes of spheres with different radii. The tutorial also includes finding the height of cones given their volumes, analyzing gasoline price trends using a graph, and solving a system of equations for bicycle and tricycle inventory in a shop.

What is the formula for the volume of a sphere?

• V = 4/3 πr^3

• V = 2πr

• V = 1/3 πr^2h

• V = πr^2h

If a sphere has a radius of 4 cm, what is its volume?

• 128/3 π cm³

• 64/3 π cm³

• 512/3 π cm³

• 256/3 π cm³

A sphere with a diameter of 6 cm has what volume?

• 54 π cm³

• 72 π cm³

• 18 π cm³

• 36 π cm³

What is the volume of a sphere with a radius of 8 cm?

• 1024/3 π cm³

• 4096/3 π cm³

• 2048/3 π cm³

• 512/3 π cm³

How do you find the volume of a cube with a side length of 8 units?

• 128 cubic units

• 512 cubic units

• 256 cubic units

• 64 cubic units

What is the volume of a sphere that fits snugly inside a cube with a side length of 8 units?

• 128/3 π units³

• 512/3 π units³

• 64/3 π units³

• 256/3 π units³

What fraction of the cube is occupied by the sphere?

• π/4

• π/2

• π/3

• π/6

If sphere A has a radius of 2 cm, what is its volume?

• 128/3 π cm³

• 64/3 π cm³

• 16/3 π cm³

• 32/3 π cm³

Sphere B has a radius of 4 cm. How many times greater is its volume compared to sphere A with a radius of 2 cm?

• 16 times

• 8 times

• 4 times

• 2 times

What is the height of cone A with a radius of 2 cm and a total volume of 192π cm³ for three cones?

• 72 cm

• 36 cm

• 64 cm

• 144 cm