An open cone has a radius of 6 cm and a hieght of 8 cm. What is its surface area in square centimetre?
the lateral area is πrs = πr√(r^2+h^2)
so plug in your numbers
An open cone has a radius of 6cm and height of 8cm.What is its surface area in square centimetre?
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The surface area of an open cone with a radius of 6 cm and a height of 8 cm can be found by adding the curved surface area (lateral area) to the area of the base.
The curved surface area (lateral area) of a cone is given by πrs, where r is the radius of the base of the cone, and s is the slant height of the cone.
The slant height of the cone can be found using the Pythagorean theorem:
s^2 = r^2 + h^2
s^2 = 6^2 + 8^2
s^2 = 100
s = 10
Therefore, the curved surface area of the cone is:
πrs = π(6)(10)
= 60π
The area of the base can be found using the formula for the area of a circle:
Area of base = πr^2
= π(6)^2
= 36π
The total surface area is the sum of the curved surface area and the area of the base:
Total surface area = curved surface area + area of base
= 60π + 36π
= 96π
= 301.6 cm^2 (rounded to one decimal place)
Therefore, the surface area of the open cone is approximately 301.6 square centimeters.