Are these correct:
3) Find the capacity in gallons of a drum that is cone-shaped if the radius is 9 feet, and the slant height is 41 feet. (first find the volume)
Volume in cubic feet = 3477.74306 cubic feet
Capacity in gallons = 26013 gallons (Round answer to the nearest gallon) (Use 1 cu ft = 7.48 gallons)
use Pythagoras to find the perpendicular height, realize that 41 is the hypotenuse.
You used 41 as the height, that is your error.
(see if you can get 3394)
adjust your capacity accordingly
To find the capacity in gallons of a cone-shaped drum, we first need to find the volume of the drum.
The volume of a cone can be found using the formula:
Volume = (1/3) * π * r^2 * h,
where r is the radius of the base of the cone and h is the height, which can be found using the slant height.
Given that the radius (r) is 9 feet and the slant height is 41 feet, we can calculate the height (h) using the Pythagorean theorem:
h = sqrt(slant height^2 - radius^2)
h = sqrt(41^2 - 9^2)
h = sqrt(1681 - 81)
h = sqrt(1600)
h = 40 feet
Now that we have the height, we can calculate the volume:
Volume = (1/3) * π * 9^2 * 40
Volume = (1/3) * π * 81 * 40
Volume = (1/3) * 3240 * π
Volume ≈ 10727.43 cubic feet
To convert this volume to gallons, we can use the conversion factor of 1 cubic foot = 7.48 gallons:
Capacity in gallons = Volume in cubic feet * 7.48
Capacity in gallons ≈ 10727.43 * 7.48
Capacity in gallons ≈ 80180.47 gallons
Since we are asked to round the answer to the nearest gallon, the capacity in gallons is approximately 80180 gallons.