Exploring Volume and Surface Area of 3D Shapes

The video tutorial covers solving problems involving the volumes of cylinders, cones, and spheres. It includes calculating the volume of a propane storage tank, determining the amount of jelly needed for a jar, finding the volume of wood left after cutting a cone from a cylinder, and calculating the water volume a trough can hold. Each problem is solved step-by-step, using formulas for volume and rounding results as needed.

What is the correct formula to calculate the volume of a cylinder?

• πr^3

• 4/3πr^3

• πr^2h

• 2πrh

Is the volume of one half-sphere more than 32.7 cubic feet?

• True

• False

• Depends on the radius

• Not enough information

For the propane storage tank, is the combined volume of the two half-spheres less than the cylinder part?

• Equal to the cylinder part

• False

• Not enough information

• True

What is the total volume of the propane storage tank?

• 65.4 cubic feet

• 137.375 cubic feet

• 32.7 cubic feet

• 202.375 cubic feet

What mistake did Isabel make in calculating the jelly needed for the jar?

• Used the wrong radius

• Did not subtract the space at the top

• Used the wrong formula for volume

• Calculated for the full height instead of the reduced height

What is the volume of the cylinder before subtracting the cone?

• 3052.08 cubic centimeters

• 2924.91 cubic centimeters

• 127.17 cubic centimeters

• 352.08 cubic centimeters

What is the correct volume of the cone that was cut out?

• 2924.91 cubic centimeters

• 127.17 cubic centimeters

• 352.08 cubic centimeters

• 3052.08 cubic centimeters

What is the final volume of the piece of wood after the cone is removed?

• 2924.91 cubic centimeters

• 352.08 cubic centimeters

• 127.17 cubic centimeters

• 3052.08 cubic centimeters

What is the correct formula to calculate the volume of water the trough can hold?

• πr^3

• 2πrh

• 1/2πr^2h

• πr^2h

What is the actual volume of water the trough will hold, rounded to the nearest whole cubic foot?

• 17 cubic feet

• 20 cubic feet

• 18 cubic feet

• 19 cubic feet