The given solid is a cone and we want to calculate its volume.
To calculate the volume of a cone, we can use the following formula.
V= 13π r^2 h
Here, r is the radius and h is the height of the cone. From the diagram, we know that the radius is r= 2inches, and the slant height is l= 5inches. We are missing the value of the height.
Let's use the Pythagorean Theorem to calculate the height of the cone. To do so, we will think of the radius and the height as the legs of a right triangle, and the slant height as the hypotenuse.
r^2+h^2=l ^2
Let's substitute 2 and 5 for r and l, respectively, and solve for h.
Note that, when solving the equation, we kept the principal root because the height must be positive. Finally, we will substitute r= 2 and h= sqrt(21) into the formula for the volume of the cone.
