Unit 5 Review - 2024-25

The volume of a cylinder is given by the formula: $$V = \text{Base Area} \times \text{Height} = \frac{1}{3} \times \text{Height} \times \text{Diameter}^2 \times \frac{\text{π}}{4}$$ .

The radius is half of the diameter. If the diameter is D, then the radius R is given by: $$R = \frac{D}{2}$$ .

The total surface area (SA) of a rectangular prism is given by the formula: $$SA = 2lw + 2lh + 2wh$$ , where l is length, w is width, and h is height.

The volume of a sphere is calculated using the formula: $$V = \frac{4}{3} \times \text{π} \times r^3$$ , where r is the radius of the sphere.

The volume of a cylinder can be expressed as: $$V = \text{Base Area} \times \text{Height}$$ . If the base area is constant, increasing the height increases the volume.

The volume of a cylinder is given by: $$V = \text{π} \times r^2 \times h$$ .

Rearranging the volume formula, the height can be found using: $$h = \frac{V}{\text{π} \times r^2}$$ .

The surface area (SA) of a cylinder is given by: $$SA = 2\text{π}r(h + r)$$ , where r is the radius and h is the height.

Using the radius is crucial because the volume formula for a sphere depends on the radius raised to the third power, which significantly affects the volume.

To estimate the height, use the formula: $$h = \frac{V}{\text{π} \times r^2}$$ and round to the nearest tenth.