QQuestion
The height of a right circular cylinder is twice the radius of the base. If the height is 6 times of the radius, then the volume of the cylinder is 539 cubic decimeter more than the previous volume. Find the height of the cylinder.
WBBSEClass 10MathematicsRight Circular Cylinder04 Mark2025 Moderate
✓Answer
Let the original radius of the base be r and the original height be h.
From the given condition:
h = 2r
The volume of a cylinder is given by:
V = π r² h
Substituting h = 2r in the volume formula:
V₁ = π r² (2r)
V₁ = 2π r³
Now, the new height is 6 times the radius, so:
h’ = 6r
The new volume is:
V₂ = π r² (6r)
V₂ = 6π r³
According to the problem, the difference in volume is 539 cubic decimeters:
V₂ – V₁ = 539
Substituting the values of V₁ and V₂:
6π r³ – 2π r³ = 539
4π r³ = 539
Substituting π ≈ \frac{22}{7} :
4 × \frac{22}{7} × r³ = 539
\frac{88}{7} × r³ = 539
Multiplying both sides by 7:
88 r³ = 3773
⇒ r³ = \frac{3773}{88}
⇒ r³ = \frac{343}{8}
⇒ r = 3.5 dm
∴ height = 2r
= 2 × 3.5
= 7 cm
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