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Question

Assertion: The total surface area of a cone whose radius is r2 and slant height 2l is (π)rl+r4.

Reason: Total surface area of cone is πr(l+r) where r is radius and l is the slant height of the cone.

Which of the following is correct?


A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

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B

If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

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C

If Assertion is correct but Reason is incorrect.

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D

If Assertion is incorrect but Reason is correct.

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Solution

The correct option is A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.


Explanation for correct option

A:

Assertion:

Step 1: Given data

Radius of original cone=r

Slant height of original cone=l

Radius of new cone=r2

Slant height of new cone=2l

New total surface area=?

Step 2: Using the formula

Total surface area of cone=πrl+πr2

Step 3: Calculating the new total surface area of cone

TSA of cone=πrl+πr2

New TSA of cone,

=πr2×2l+πr22=πr2l2+r4=πrl+r4

Thus, the total surface area of a cone whose radius is r2 and slant height 2l is (π)rl+r4.

Assertion is correct.

Reason:

Step 1: Given data

Radius of original cone=r

Slant height of original cone=l

total surface area=?

Step 2: Using the formula

Curved surface area of cone=πrl

Area of circle=πr2

Step 3: Calculating the total surface area of cone

CSA of cone=πrl

We know, that base of a cone is a circle.

So, TSA of cone=CSA of cone+Area of circle

TSA of cone=πrl+πr2

Taking πrcommon in the above equation

Therefore,

TSA of cone=πr(l+r)

Thus, the total surface area of cone is πr(l+r) where r is radius and l is the slant height of the cone.

Reason is correct.

Since, Reason is in relation to the Assertion. Thus, Reason is the correct explanation of Assertion.

Hence, option A is correct.


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