Answer:
The volume is about 5275.2 m^3
Explanation:
The formula for volume of a cone is given by:
V = 1/3πr^2h, where
- V is the volume in cubic units,
- r is the radius.
- and h is the height
Step 1: We're not given the radius, but we see that the slant height and the regular height (altitude) are parts of a right triangle inside the cone, where
- the slant height is the hypotenuse measuring 37 m,
- and the altitude is a leg measuring 35 m.
Since we're working with a right triangle, we can find the other leg (our radius) using the Pythagorean theorem, which is:
a^2 + b^2 = c^2, where
- a and b are the shorter sides called legs (they form the right angle),
- and c is the longest side called the hypotenuse (opposite the right angle)
Thus, we can plug in 35 for a and 37 for c, allowing us to solve for b, the measure of our radius:
1.1 Plug in 35 for a and 37 for c. Then simplify:
35^2 + b^2 = 37^2
1225 + b^2 = 1369
1.2 Subtract 1225 from both sides:
(1225 + b^2 = 1369) - 1225
b^2 = 144
1.3 Take the square root of both sides to isolate and solve for b, the measure of the radius:
√b^2 = ± √144
b = ± 12
Although taking the square root of a number gives us both a positive and negative answer, you can't have a negative measure, so b = 12 and thus the radius, r, = 12 m
Step 2:
Plug in 3.14 for π, 12 for r, and 35 for h in the volume formula. Then simplify and round to find the volume of the cone:
V = 1/3(3.14)(12)^2(35)
V = 157/150 * 144 * 35
V = 150.72 * 35
V = 5275.2 m^3
Thus, the volume of the cone is 5275.2 m^3