The given solid is a cone. It has a height of 22 centimeters and a diameter of 10 centimeters. The length of the slant height is unknown.
Let's first calculate the lateral area and then the surface area.
Lateral Area
To calculate the lateral area of a cone, we can use the known formula where r is the radius of the base and l is the slant height.
L=π rl
From the diagram, we know that the diameter of the cone's base is 10. By dividing by 2, we get the radius of the base.
r=10/2= 5
Therefore, the radius of the base is 5 centimeters.
Also, we can see a right triangle formed by the height of the cone, the radius of the base, and the slant height.
The lateral area of the cone is about 354.4 square centimeters.
Surface Area
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
Earlier, we found that r= 5 and π rl ≈ 354.4. Let's substitute these values into the formula to calculate S.
