Question
Download Solution PDFThe sum of the radius of the base and the height of a solid right circular cylinder is 39 cm. Its total surface area is 1716 cm2. What is the volume (in cm3) of the cylinder? (Take π = \(\frac{22}{7}\))
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Sum of radius and height of the cylinder = 39 cm
Total surface area of the cylinder = 1716 cm2
Concept used:
Total surface area of a cylinder = 2πr(h + r)
Volume = πr2h
Here,
r = radius
h = height
Calculation:
Let the radius and the height of the cylinder be r and h,
According to the question,
2πr(h + r) = 1716 ----(i)
(h + r) = 39 ----(ii)
Putting the value of eq (ii) in eq (i) we get,
2πr × 39 = 1716
⇒ 2πr = 1716/39
⇒ 2πr = 44
⇒ πr = 22
⇒ r = 22 × (7/22)
⇒ r = 7
So, radius = 7 cm
Now, by putting the value of r in the eq (ii) we get
h + 7 = 39
⇒ h = 32
So, height = 32 cm
Now, volume = (22/7) × 72 × 32
⇒ 22 × 7 × 32
⇒ 4928
So, volume of the cylinder = 4928 cm3
∴ The volume (in cm3) of the cylinder i 4928.
Last updated on Jul 5, 2025
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