The given solid is a cone. To calculate the surface area of a cone, we can use the known formula where r is the radius of the base and l is the slant height of the cone.
S=π rl+π r^2
From the diagram, we know that the diameter of the cone's base is 8centimeters. By dividing it by 2, we get the radius of the base.
r=8/2 ⇔ r= 4cm
To find the slant height, we can use the Pythagorean Theorem. Therefore, the slant height l is the hypotenuse. The height and radius of the cone are the legs. Let's use these given values to solve for l.
Therefore, the slant height of the cone is about 7.2cm. Note that, when solving the above equation, we kept the principal root. This is because l must be positive. By substituting r for 4 and l for 7.2 into the formula, we can calculate S.
