A slow cooker is used to cook food slowly. The diameter of a slow cooker is 15 inches, and the volume is 1400 cubic inches. A second slow cooker has a diameter that is 20% greater.
What is the volume of the larger pot?
Are they the same height?
To find the volume of the larger slow cooker, we can use the relationship between the diameter and the volume of a cylinder. The volume of a cylinder can be calculated using the formula:
V = π * r^2 * h
Where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base of the cylinder, and h is the height of the cylinder.
Given that the diameter of the first slow cooker is 15 inches, the radius (r) is half of the diameter, which is 15 / 2 = 7.5 inches.
The volume of the first slow cooker is given as 1400 cubic inches. Therefore, we can calculate the height (h) of the first slow cooker using the formula:
1400 = π * (7.5)^2 * h
Simplifying the equation, we get:
1400 = 3.14159 * 7.5^2 * h
Dividing both sides of the equation by (3.14159 * 7.5^2), we can solve for h:
h = 1400 / (3.14159 * 7.5^2)
Plugging this value of h back into the volume formula, we can calculate the height (h) of the slow cooker:
V = π * (r)^2 * h
So, the volume (V) of the larger slow cooker can be found by increasing the diameter of the first slow cooker by 20%:
New diameter = 15 * (1 + 0.20) = 18 inches.
Using the same formula for the volume, the radius (r) of the larger slow cooker is 18 / 2 = 9 inches.
Now we can calculate the volume of the larger slow cooker:
V = π * (9)^2 * h
Since we know the volume of the first slow cooker is 1400 cubic inches, we can plug in the known values:
1400 = π * (9)^2 * h
Simplifying the equation:
1400 = 3.14159 * 9^2 * h
Dividing both sides of the equation by (3.14159 * 9^2), we can solve for h:
h = 1400 / (3.14159 * 9^2)
Finally, we can calculate the volume (V) of the larger slow cooker by substituting the values of the radius (r) and height (h) into the volume formula:
V = π * (9)^2 * h
By evaluating this equation, we can find the volume of the larger slow cooker.