Total surface area of a right circular cylinder is 1540 cm? If its height is four times the radius, then find
the volume of the cylinder,
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Total surface area of a right circular cylinder is 1540 cm? If its height is four times the radius, then find
the volume of the cylinder,
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Verified answer
Given
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To Find
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Solution
To find the volume of the cylinder it is essential to find the height and radius of the cylinder first.
Formula to find the Area of a Right Circular Cylinder → 2πr (r + h)
Area of the Given Right Circular Cylinder → 1540 cm²
Let the Radius be 'r'
Height → 4r
Now let's solve the below equation to find the radius and height.
2πr (r + 4r) = 1540
Step 1: Simplify the equation.
⇒ 2πr (r + 4r) = 1540
⇒ 2πr (5r) = 1540
⇒ 10πr² = 1540
Step 2: Divide 10 from both sides of the equation.
⇒ 10πr² ÷ 10 = 1540 ÷ 10
⇒ πr² = 154
Step 3: Multiply 7/22 to both sides of the equation.
⇒
⇒ r² = 7 × 7
⇒ r² = 49
Step 4: Find square root of 49.
⇒ r² = 49
⇒ r = √49
⇒ r = 7
∴ The radius → r = 7
∴ The height → 4r = 4(7) = 28
Now let's find the volume of the cylinder.
Formula to find the Volume of Cylinder → πr²h
Volume of Given Cylinder ⇒ π × (7)² × 28
⇒ π × 49 × 28
⇒
⇒ 22 × 7 × 28
⇒ 4312 cm³
∴ The volume of the cylinder is 4312 cm³
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