Composite Solids

A composite solid is a three-dimensional shape that is made up of two or more basic geometric shapes, such as cylinders, cones, and spheres.

The volume of a cylinder is calculated using the formula: $$V = \text{Base Area} \times \text{Height} = \text{π}r^2h$$ , where r is the radius and h is the height.

The volume of a cone is given by the formula: $$V = \frac{1}{3} \text{π}r^2h$$ , where r is the radius of the base and h is the height.

To find the volume of a composite solid, calculate the volume of each individual shape and then sum them up.

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

Using the formula $$V = \text{π}r^2h$$ , the volume is approximately $$V = \text{π}(3^2)(5) \text{ cm}^3 \text{ or } 45\text{π} \text{ cm}^3$$ .

The volume of a cone is one-third the volume of a cylinder with the same base and height: $$V_{cone} = \frac{1}{3} V_{cylinder}$$ .

To round a volume to the nearest whole number, look at the first decimal place: if it's 5 or more, round up; if it's less than 5, round down.

To find the volume, calculate the volume of the cylinder and the hemisphere separately, then add them together.

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.