Volume and Geometry Problems

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 two spheres. The tutorial also includes finding the height of cones given their volumes, analyzing gasoline prices over time, and solving a system of equations to determine the number of bicycles and tricycles in a store.

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

• 36 π cm³

• 288 π cm³

• 64/3 π cm³

• 256/3 π cm³

If a sphere has a diameter of 6 cm, what is its volume?

• 54 π cm³

• 36 π cm³

• 18 π cm³

• 72 π cm³

What is the side length of a cube with a volume of 512 cubic units?

• 6 units

• 8 units

• 12 units

• 10 units

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

• 1/3

• 1/2

• π/6

• π/4

How many times greater is the volume of a sphere with a radius of 4 cm compared to one with a radius of 2 cm?

• 4 times

• 2 times

• 8 times

• 6 times

What is the volume of a sphere with a radius of 2 cm?

• 32/3 π cm³

• 256/3 π cm³

• 64/3 π cm³

• 128/3 π cm³

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

• 64 cm

• 36 cm

• 144 cm

• 72 cm

If cone B has a radius of 3 cm, what is its height given the total volume of 192π cm³ for three cones?

• 72 cm

• 144 cm

• 64 cm

• 36 cm

How many bicycles are in the store if there are 18 tricycles?

• 220

• 200

• 178

• 160

What is the equation representing the number of bicycles in terms of tricycles?

• b = 2t - 10

• b = 2t + 10

• b = 10t - 2

• b = 10t + 2