A conical tent made of canvas has a base that is 26 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 p.
A = pi r (r+s)
just plug in the numbers
remember r=13, not 26.
Liar liar pants on fire
To find the area of the canvas, including the floor, we need to calculate the total surface area of the conical tent. The surface area of a cone consists of three parts: the base, the lateral surface, and the slanted surface.
First, let's find the area of the base. The base of the cone is a circle, and the formula to find the area of a circle is A = πr^2, where A is the area and r is the radius. We know that the base has a diameter of 26 feet, so the radius would be half of that, which is 26/2 = 13 feet. Thus, the area of the base is A_base = 3.14 * (13^2).
Next, we need to find the lateral surface area. The lateral surface of the cone is a curved surface that makes up the sides of the cone. The formula for the lateral surface area is A_lateral = πr * slant height. In this case, the radius is still 13 feet, and the slant height is given as 14 feet. So, the lateral surface area is A_lateral = 3.14 * 13 * 14.
Finally, we can calculate the total surface area of the canvas, including the floor, by adding together the areas of the base, the lateral surface, and the slanted surface. Since the slanted surface is the same as the lateral surface, we can combine them. Therefore, the total surface area is A_total = A_base + A_lateral.
Let's plug in the numbers and calculate:
A_base = 3.14 * (13^2) = 530.66 square feet (rounded to the nearest whole unit)
A_lateral = 3.14 * 13 * 14 = 573.56 square feet (rounded to the nearest whole unit)
A_total = A_base + A_lateral = 530.66 + 573.56 = 1104.22 square feet (rounded to the nearest whole unit)
Therefore, the area of the canvas, including the floor, to the nearest whole unit is approximately 1104 square feet.