To find: The slant height of the largest tent
Answer to Problem 21PPS
The slant height of the largest cone is approximately 48.7cm.
Explanation of Solution
Given:
A can of water repellant says it will seal a canvas that is 50 feet by 60 feet.
Diameter of cone is 30 feet.
Formula used:
The lateral area L of a cone is given by the formula
The surface area S of acone is given by the formula
Calculation:
Consider a canvas that is 50 ft. by 30 ft. Also consider the diameter of the cone is 30 ft.
The given figure is a cone.
The objective is to find the slant height of the largest tent that can be made with the given surface.
Let l represent the slant height the cone.
Thus,
Since radius is half the diameter, so the radius of the cone is
Put r=15 andl=linthe surface area formula to find the surface area of the cone.
Thus,
The area of the canvas is
Since, the canvas area is the surface area of the cone, so
Therefore, the slant height of the largest cone is approximately 48.7cm.
Conclusion:
Therefore, the slant height of the largest cone is approximately 48.7cm.
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