Question
Download Solution PDFA solid is in the form of a cylinder with hemispherical ends. The diameter of the cylinder is 1/3 of its height (excluding the hemispherical ends). The total length of the solid including the hemispherical ends is 56 cm. What is the surface area of the solid?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The diameter of the cylinder = Height/3
Total length = 56 cm
Formula:
Surface area of cylinder = 2πrh
Surface area of hemisphere = 2πr2
Calculation:
Let the diameter be 2x
Height of the cylinder = 6x
The total length of the solid including the hemispherical ends = 56 cm
⇒ 6x + 2x = 56
⇒ x = 7 cm
The surface area of cylinder = 2π × 7 × 42
The surface area of cylinder = 1848 cm2
Surface area of one hemisphere = 2π × 49 = 308 cm2
Surface area of two hemisphere = 308 × 2 = 616 cm2
∴ The surface area of the solid = 1848 + 616 = 2464 cm2
Last updated on Jul 7, 2025
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