Cavalieri’s Principle and Surface Area Exam Review

Front

What is Cavalieri's Principle?

Back

Cavalieri's Principle states that if two solids have the same height and the same cross-sectional area at every level, then they have the same volume.

Front

What is a cross-section?

Back

A cross-section is the intersection of a solid object with a plane, resulting in a two-dimensional shape.

Front

What shapes can a cross-section take?

Back

Common shapes of cross-sections include square, rectangle, triangle, and circle.

Front

How do you find the surface area of a prism?

Back

To find the surface area of a prism, calculate the area of all its faces and sum them up.

Front

What is the formula for the surface area of a rectangular prism?

Back

Surface Area = 2(lw + lh + wh), where l = length, w = width, h = height.

Front

What is the total surface area of a cylinder?

Back

Total Surface Area = 2πr(h + r), where r = radius and h = height.

Front

If two prisms have the same height but different cross-sectional areas, will they have the same volume?

Back

No, they will not have the same volume because their cross-sectional areas are different.

Front

What is the surface area of a cube with side length 5 cm?

Back

Surface Area = 6s² = 6(5)² = 150 cm².

Front

What is the relationship between volume and surface area?

Back

Volume measures the amount of space inside a solid, while surface area measures the total area of its outer surfaces.

Front

How do you calculate the surface area of a triangular prism?

Back

Surface Area = base area + lateral area, where lateral area is the sum of the areas of the three rectangular faces.