Question

Find the volume of the solid that is created when you rotate the figure around the line: round to the nearest hundredth (two decimal places)

Answer 1

Answer:5

Explanation:

Answer 2

The volume of the solid created when the figure is rotated around the line is 13.09 cubic centimeter, rounded to the nearest hundredth.

When you rotate a two-dimensional figure around a line to create a three-dimensional solid, the volume of the solid depends on the shape of the original figure and the axis of rotation. From the description, it appears that the figure is a triangle, and if we rotate a right triangle around one of its legs, we create a cone.

The volume V of a cone is given by the formula:

`\[ V = (1)/(3) \pi r^2 h \]`

where r is the radius of the base of the cone, and h is the height of the cone.

Assuming that the triangle is rotated around the leg that is 2 cm long, which then becomes the height h of the cone, and the leg that is 5 cm long becomes the slant height (not used directly in the volume formula), the leg opposite the right angle would be the diameter of the cone's base. Therefore, the radius r would be half of that length, or 2.5 cm.

Using these values, we can calculate the volume of the cone:

`\[ r = 2.5 \text{ cm} \]\[ h = 2 \text{ cm} \]`

`\[ V = (1)/(3) \pi (2.5)^2 * 2 \]`

V=13.09 cubic centimeter