the total surface area of a cylinderical can, whose height is equal to the radius of the base is 2646 cm, find its volume.
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2πr^2 + 2πrh = 2646
Now, we know that h=r, so that means
4πr^2 = 2646
r^2 = 2646/4π =
The volume v is
v = πr^2 h = πr^3 = π(2646/4π)^3/2 = 27783 √(3/8π)
To find the volume of a cylindrical can, we need to know the height and radius of the base. In this case, the height is given as equal to the radius.
Let's call the height and radius of the base both "h". So, the radius (r) of the base is also "h".
The total surface area (TSA) of a cylinder can be calculated using the formula:
TSA = 2πrh + πr^2
In this case, the TSA is given as 2646 cm. So, we can write the equation as:
2646 = 2πrh + πh^2
To find the volume, we need the formula for the volume of a cylinder, which is:
Volume (V) = πr^2h
Since we know that r = h, we can rewrite it as:
V = πh^2h = πh^3
Now, we need to solve the equation for h and find its value to calculate the volume.
2646 = 2πrh + πh^2
2646 = 2πh^2 + πh^2
2646 = 3πh^2
Hence, 3πh^2 = 2646
Divide both sides of the equation by 3π:
h^2 = 2646 / (3π)
h^2 = 2646 / (3 * 3.14159)
h^2 ≈ 281.627
To find h, take the square root of both sides:
h ≈ √281.627
Approximately, h ≈ 16.8 cm
Now that we have h, we can find the volume using the formula:
V = πh^3
Substituting the approximate value of h:
V ≈ π(16.8)^3
V ≈ π(4745.344)
V ≈ 14915.478 cm^3
Therefore, the volume of the cylindrical can is approximately 14915.478 cm^3.