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If M be the volume of cone and N be the curved surface area of a cone of dimensions p, q and r where p is the radius, q is the height and r is the slant height of a cone, then 1/M is equal to
- a)N (3r)/q r
- b)3N/p q
- c)3r/q r
- d)1/N [3r/p q]
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If M be the volume of cone and N be the curved surface area of a cone ...
Since, M = 1/3 ∏ r² h = 1/3 ∏ p² q
and N = ∏rl = ∏pr
Now, N/M = ∏pr/ 1/3 ∏ p² q
Therefore, 1/M = 1/N [3r/p q]
Most Upvoted Answer
If M be the volume of cone and N be the curved surface area of a cone ...
Understanding the Cone's Volume and Curved Surface Area
To solve the problem, we need to understand the formulae for the volume and curved surface area of a cone.
1. Volume of the Cone (M)
The volume (M) of a cone is given by the formula:
- M = (1/3) * π * p² * q
Where:
- p = radius of the base
- q = height of the cone
2. Curved Surface Area of the Cone (N)
The curved surface area (N) of a cone is calculated using the formula:
- N = π * p * r
Where:
- r = slant height of the cone
3. Relationship Between M and N
To find 1/M, we first express M in terms of p and q:
- 1/M = (3)/(π * p² * q)
Now, substituting the expression for N:
- N = π * p * r
4. Finding the Relationship
We can express r in terms of N:
- r = N / (π * p)
Now substituting r back into the equation for 1/M:
- 1/M = (3)/(π * p² * q) becomes
- 1/M = (3 * N) / (q * p * r)
Finally, rearranging gives us:
- 1/M = 1/N * (3r)/(pq)
Thus, we conclude that:
5. Correct Option
From the derivation, we see that:
- 1/M = 1/N * (3r)/(pq)
This confirms that the correct answer is option 'D'.
To solve the problem, we need to understand the formulae for the volume and curved surface area of a cone.
1. Volume of the Cone (M)
The volume (M) of a cone is given by the formula:
- M = (1/3) * π * p² * q
Where:
- p = radius of the base
- q = height of the cone
2. Curved Surface Area of the Cone (N)
The curved surface area (N) of a cone is calculated using the formula:
- N = π * p * r
Where:
- r = slant height of the cone
3. Relationship Between M and N
To find 1/M, we first express M in terms of p and q:
- 1/M = (3)/(π * p² * q)
Now, substituting the expression for N:
- N = π * p * r
4. Finding the Relationship
We can express r in terms of N:
- r = N / (π * p)
Now substituting r back into the equation for 1/M:
- 1/M = (3)/(π * p² * q) becomes
- 1/M = (3 * N) / (q * p * r)
Finally, rearranging gives us:
- 1/M = 1/N * (3r)/(pq)
Thus, we conclude that:
5. Correct Option
From the derivation, we see that:
- 1/M = 1/N * (3r)/(pq)
This confirms that the correct answer is option 'D'.
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If M be the volume of cone and N be the curved surface area of a cone of dimensions p, q and r where p is the radius, q is the height and r is the slant height of a cone, then 1/M is equal toa)N (3r)/q rb)3N/p qc)3r/q rd)1/N [3r/p q]Correct answer is option 'D'. Can you explain this answer?
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