steel is $50 per cubic foot. What is cost of cone with radius 7.5 inches and 25 inches height?
Work out all dimensions in feet.
r=7.5 inches = 7.5/12=0.625'
h=25 inches = (25/12)'
Volume = (1/3) π r² h
and
from the price of $50/ft², we get
Cost=volume*price
=(1/3) π r² h * 50
Round the answer to two decimal places (to the cent).
I'll leave it to you to work with the buttons of your calculator.
Thank you, it works.
You're welcome!
To calculate the cost of the cone, we first need to convert the measurements to the same unit. In this case, let's convert the radius from inches to feet.
Given:
Radius (r) = 7.5 inches
Height (h) = 25 inches
Cost of steel = $50 per cubic foot
Step 1: Convert the radius from inches to feet
Since 1 foot contains 12 inches, we divide the radius by 12 to convert it to feet:
Radius (r) = 7.5 inches / 12 = 0.625 feet
Step 2: Calculate the volume of the cone
The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where:
V = Volume
π = Pi (approximately 3.14159)
r = Radius
h = Height
Substituting the values we have:
V = (1/3) * 3.14159 * (0.625 feet)^2 * 25 inches
Step 3: Convert the height from inches to feet
Since 1 foot contains 12 inches, we divide the height by 12 to convert it to feet:
Height (h) = 25 inches / 12 = 2.083 feet
V = (1/3) * 3.14159 * (0.625 feet)^2 * 2.083 feet
Step 4: Calculate the volume
V = (1/3) * 3.14159 * (0.625 feet)^2 * 2.083 feet ≈ 0.6875 cubic feet
Step 5: Calculate the cost of the cone
The cost of the cone is determined by multiplying the volume with the cost per cubic foot:
Cost = Volume * Cost per cubic foot
Cost = 0.6875 cubic feet * $50 per cubic foot
Calculating the final result:
Cost = $34.375
Therefore, the cost of the cone with a radius of 7.5 inches and a height of 25 inches is approximately $34.375.