Is spyglass in the shape of a cone has a slant height of 18 cm and a radius of 6 cm what is the surface area of the spyglass glass?
To find the surface area of the spyglass, we need to calculate the curved surface area of the cone and the surface area of the base.
Curved Surface Area of the Cone:
The curved surface area of a cone can be calculated using the formula:
CSA = π * r * l
where r is the radius and l is the slant height.
CSA = π * 6 cm * 18 cm = 108π cm² (rounded to two decimal places)
Surface Area of the Base:
The base of the spyglass is a circle with a radius of 6 cm.
The formula for the area of a circle is:
A = π * r²
A = π * 6 cm * 6 cm = 36π cm² (rounded to two decimal places)
Total Surface Area:
Surface Area = CSA + Base Area
Surface Area = 108π cm² + 36π cm² = 144π cm² (rounded to two decimal places)
Therefore, the surface area of the spyglass is approximately 144π cm².