Question
Download Solution PDFThe height of a solid cylinder is 30 cm and the diameter of its base is 10 cm. Two identical conical holes each of radius 5 cm and height 12 cm are drilled out. What is the surface area (in cm2) of the remaining solid?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Height of cylinder = 30 cm
Radius of cylinder = 5 cm
Height of cone = 12 cm
Radius of cone = 5 cm
Formula used:
The surface area of cylinder = 2πrh
The surface area of cone = πrl
l2 = h2 + r2
Where,
l = slant height of the cone
h = height
r = radius
Calculation:
l2 = h2 + r2
⇒ l2 = 122 + 52
⇒ l2 = 144 + 25
⇒ l = 13 cm
The surface area of the remaining figure = surface area of cylinder + 2 × Curved surface area of the cone
⇒ 2πrh + 2πrl
⇒ 2πr(h + l)
⇒ 2π × 5(30 + 13)
⇒ 430π
∴ The surface area of the remaining solid is 430π.
Additional Information
When the cones are drilled out then the volume of a cylinder is decreasing. But the surface area will increase. Surface area means the area which we can touch. When the cones drilled out then we can touch both outer and the inner surface. So we have to add both surface areas.
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