A conical tent made of canvas has a base that is 20 feet across and a slant height of 14 feet. To the nearest whole unit, what is the area of the canvas, including the floor? Use 3.14 for pi.
A. 754 ft^2
B. 1,193 ft^2
C. 2,135 ft^2
D. 534 ft^2
This question stumps me...please help!
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To find the area of the canvas, including the floor of the conical tent, we need to calculate the area of the base and the curved surface area of the cone.
First, let's find the area of the base. The base of the conical tent is a circle, and the formula to calculate the area of a circle is A = πr^2, where A is the area, and r is the radius.
Given that the base has a diameter of 20 feet, we can find the radius by dividing the diameter by 2. Therefore, the radius (r) is 20/2 = 10 feet.
Now, we can calculate the area of the base:
A_base = π(10^2)
A_base = 3.14 * (10^2)
A_base = 3.14 * 100
A_base ≈ 314 square feet
Next, let's find the curved surface area of the cone. The curved surface area of a cone is given by the formula A_cone = πrl, where r is the radius and l is the slant height.
Given that the radius (r) is 10 feet and the slant height (l) is 14 feet, we can calculate the curved surface area:
A_cone = 3.14 * 10 * 14
A_cone = 3.14 * 140
A_cone ≈ 439.6 square feet
Finally, to find the total area of the canvas, including the floor, we add the area of the base and the curved surface area of the cone:
Total area = A_base + A_cone
Total area ≈ 314 + 439.6
Rounded to the nearest whole unit, the area of the canvas is:
Total area ≈ 753.6 square feet
Therefore, the answer is approximately 754 square feet (option A).