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Question
A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is `pir [sqrt(r^2 + h^2) + 3r + 2h]`.
Options
True
False
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Solution
This statement is False.
Explanation:
When a solid cone is placed over a solid cylinder of same base radius, the base of cone and top of the cylinder will not be covered in total surface area.
Since the height of cone and cylinder is same,
We get,
Total surface area of cone = πrl + πr2, where r = base radius and l = slant height
Total surface area of shape formed = Total surface area of cone + Total surface area of cylinder – 2(Area of base)
Total surface area of cylinder = 2πrh + 2πr2h, where r = base radius and h = height
= πr(r + l) + (2πrh + 2πr2) – 2(πr2)
= πr2 + πrl + 2πrh + 2πr2 – 2πr2
= πr(r + l + h)
= `pi"r"("r" + sqrt("r"^2 + "h"^2) + 2"h")`
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