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Question
The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km2. Find the height of the mountain.
Solution
Let r, h and l be the base radius, the height and the slant height of the conical mountain, respectively.
As, the area of the base = 1.54 Km2
`rArr pir^2 = 1.54`
`rArr 22/7xx r^2 = 1.54`
`rArr r^2 = (1.54xx7)/22`
`rArr r2 = 0.49`
`rArr r = sqrt(0.49)`
`rArr = 0.7 "Km"`
Now ,
`h = sqrt(l^2 - r^2)`
`= sqrt(2.5^2 - 0.7^2)`
`=sqrt(6.25-0.49)`
`= sqrt(5.76)`
`=2.4 "Km"`
So, the height of the mountain is 2.4 km.
Now, the volume of the solid cylinder = πr2 h
`= 22/7 xx 7xx 7xx30`
= 4620 m3
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Assertion (A)
The outer surface of a hemisphere of radius 7 cm is to be painted. The total cost of painting at Rs 5 per cm2 is Rs 2300.
Reason (R)
The total surface area of a hemisphere is 3π r2.
- Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- Assertion (A) is true and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
