Volume of Prisms and Cylinders
Volume of prisms and cylinders equals base area × height. Find the flat base area, then multiply by the height; a 20 cm² base 3 cm tall gives 60 cm³. A cylinder has a circular base of area πr², so V = πr²h.
Video Lesson
Watch and learn the basics
🎬 Did this video explain it clearly?
Flashcards
Review key concepts visually
%20Volume%20of%20Prisms%20and%20Cylinders.webp)
%20Volume%20of%20Prisms.webp)
%20Volume%20of%20Cylinders.webp)
Volume of Prisms and Cylinders
- The volume of any prism or cylinder is
- B is the area of the base, and h is the perpendicular height
Finding the Volume of a Prism
- First, find the area of the base (e.g., area of the triangle)
- Then multiply this area by the height of the prism (i.e., the distance between the two parallel faces)
Finding the Volume of a Cylinder
- The base of a cylinder is a circle, so
- Multiply B by the height of the cylinder to get the volume:
Practice Questions
Test your understanding
What is the formula for the volume of a prism?
Correct! 🎉 +10 pointsNot quite right
The volume of a prism is calculated by multiplying the area of the base, B, by the height, h. So, the formula is .
What is the volume of a prism with a base of and a height of ?
Correct! 🎉 +10 pointsNot quite right
The formula for the volume of a prism is . Substituting the given values, we get .
What is the volume of a cylinder with a radius of and a height of ?
Correct! 🎉 +20 pointsNot quite right
The formula for the volume of a cylinder is . Substituting the values, we get .
What is the volume of a cylinder with a radius of and a height of ?
Correct! 🎉 +20 pointsNot quite right
The formula for the volume of a cylinder is . Substituting the values, we get .
What is the volume of a cylinder with a diameter of and a height of ?
Correct! 🎉 +20 pointsNot quite right
The formula for the volume of a cylinder is . The diameter is , so the radius is cm. Substituting into the formula, we get .
A prism has a triangular base with a base length of and a height of . The height of the prism is . What is the volume of the prism?
Correct! 🎉 +30 pointsNot quite right
First calculate the area of the triangular base using the formula × base × . Now, multiply the base area by the height of the prism: .
Want to see the full working?
Interactive Activity
Explore volume of prisms and cylinders by adjusting dimensions
Loading interactive widget...
Students Also Ask
The questions students bump into most on this topic
The volume of a prism equals the area of its base multiplied by its height, written as V = B × h. The base is one of the two identical end faces, and the height is the distance between them. This rule works for any prism.
A cylinder uses the same rule as a prism, so its volume equals the base area times the height. Because the base is a circle, its area is πr², giving the formula V = πr² × h. You multiply the circle's area by the height.
First find the area of the triangular base using half its base times its perpendicular height. Then multiply that base area by the length of the prism, the distance between its two triangular faces. The result is the volume in cubic units.
No, a cylinder is not a prism, but it shares similar properties with one. Because of this, you find its volume the same way as a prism: multiply the area of the base by the height. The base of a cylinder is a circle.
The height of a prism is the perpendicular distance between its two identical bases. These bases are parallel and exactly opposite each other, and the edges joining them all share this same length. You multiply the height by the base area to find the volume.