Prisms and Cylinder Review

A prism is a solid geometric figure with two parallel, congruent bases connected by rectangular or parallelogram faces.

The volume of a rectangular prism is calculated using the formula: $$V = l \times w \times h$$ , where l is length, w is width, and h is height.

The volume of a triangular prism is calculated using the formula: $$V = \frac{1}{2} \times b \times h \times L$$ , where b is the base of the triangle, h is the height of the triangle, and L is the length of the prism.

The area of a triangle is calculated using the formula: $$A = \frac{1}{2} \times b \times h$$ , where b is the base and h is the height.

A cylinder is a three-dimensional shape with two parallel circular bases connected by a curved surface.

The volume of a cylinder is calculated using the formula: $$V = \text{Area of base} \times h = \text{Area of circle} \times h = \frac{1}{4} \times \text{d}^2 \times \text{h} \times \frac{\text{π}}{4}$$ , where d is the diameter and h is the height.

To compare the volumes of two cylinders, calculate the volume of each using the formula $$V = \text{Area of base} \times h$$ and compare the results.

The volume of a prism increases with an increase in height, assuming the base area remains constant.

The base shape determines the area used in the volume formula; different shapes will yield different base areas, affecting the overall volume.

A rectangular prism has rectangular bases, while a triangular prism has triangular bases.