Volume and Properties of Prisms

The video tutorial explains how to calculate the volume of different geometric shapes, including prisms, pyramids, cylinders, cones, and spheres. It provides a step-by-step guide to solving word problems involving these shapes, focusing on the formulas for volume calculation. The tutorial includes examples of finding the volume of a square pyramid and a triangular prism, using mathematical principles such as the 30-60-90 triangle rule and the Pythagorean theorem.

Which of the following shapes is NOT mentioned in the introduction as one whose volume can be calculated?

• Pyramid

• Prism

• Cube

• Sphere

What is the base shape of the prism in the word problem?

• Circle

• Triangle

• Square

• Rectangle

If the volume of a prism is 90 cm³, what is the volume of a related pyramid with the same base and height?

• 60 cm³

• 30 cm³

• 90 cm³

• 120 cm³

What is the formula for the volume of a pyramid?

• 1/2 base area times height

• Base area times height

• 1/3 base area times height

• Base area plus height

What is the side length of the equilateral triangle base of the triangular prism?

• 3 meters

• 6 meters

• 4 meters

• 5 meters

What is the height of the triangular prism?

• 11 meters

• 10 meters

• 9 meters

• 8 meters

Which mathematical rule is used to find the height of the equilateral triangle in the prism?

• Sine rule

• Pythagorean theorem

• 30-60-90 triangle rule

• 45-45-90 triangle rule

What is the calculated height of the equilateral triangle in the triangular prism?

• 2.5

• 3.0

• 3.5

• 4.0

What is the base area of the equilateral triangle in the triangular prism?

• 6

• 5

• 8

• 7

What is the final volume of the triangular prism?

• 90 meters cubed

• 80 meters cubed

• 70 meters cubed

• 60 meters cubed