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 = cubic feet
Capacity in gallons = gallons (Round answer to the nearest gallon) (Use 1 cu ft = 7.48 gallons)
The height of the cone can be obtained from the Pythagorean relationship:
h^2 = 41^2 - 9^2 = 1600
h = 40 ft
Volume = (1/3) pi r^2 h = 3393 ft^3 = 25,379 gallons
you did 40 ft not 41 i got 3475 ft^3 but i don't know how you found gallons
40 ft is the true cone height from bottom to top. The slant height is measured along the slope.
I converted to gallons using the conversion factor that was provided by you.
(Use 1 cu ft = 7.48 gallons)
To find the volume of the cone-shaped drum, we can use the formula:
Volume of a cone = (1/3) *π * r^2 * h
where:
- r is the radius of the base of the cone
- h is the height of the cone (equal to the slant height in this case)
Given that the radius (r) is 9 feet and the slant height (h) is 41 feet, we can plug these values into the formula:
Volume = (1/3) * π * (9^2) * 41
Calculating this gives us the volume in cubic feet.
Volume ≈ 4410.47 cubic feet
Next, we need to convert the volume from cubic feet into gallons. We can use the conversion factor of 1 cubic foot = 7.48 gallons for this.
Capacity in gallons = 4410.47 cubic feet * 7.48 gallons/cubic foot
Calculating this gives us the capacity of the drum in gallons.
Capacity ≈ 32,914.15 gallons
Rounded to the nearest gallon, the capacity of the drum is approximately 32,914 gallons.