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The questions given below contain two st...

The questions given below contain two statement numbered I and II giving certain data. You have to decide whether the data given in the statements are sufficient to answer the question. Give answer.
What is the height of a cylinder? (in m)
I. The volume of the cylinder is 4158 `m^3`
II. The total surface area of the cylinder is 1485`m^2`.

A

statement I alone is sufficient but statement II alone is not sufficient.

B

statement II alone is sufficient but statement I alone is not sufficient.

C

either statement I or II is sufficient

D

both statements I and II together are not sufficient.

Text Solution

AI Generated Solution

The correct Answer is:
To determine the height of a cylinder based on the provided statements, we need to analyze the information given in each statement and see if they can help us find the height. ### Step-by-Step Solution: 1. **Understanding the Volume of the Cylinder**: - The formula for the volume \( V \) of a cylinder is given by: \[ V = \pi r^2 h \] - From Statement I, we know that the volume of the cylinder is \( 4158 \, m^3 \). Thus, we can write: \[ \pi r^2 h = 4158 \] - This equation has two variables: \( r \) (radius) and \( h \) (height). 2. **Understanding the Total Surface Area of the Cylinder**: - The formula for the total surface area \( A \) of a cylinder is given by: \[ A = 2\pi r (r + h) \] - From Statement II, we know that the total surface area of the cylinder is \( 1485 \, m^2 \). Thus, we can write: \[ 2\pi r (r + h) = 1485 \] - This equation also has two variables: \( r \) (radius) and \( h \) (height). 3. **Combining the Two Statements**: - We have two equations: 1. \( \pi r^2 h = 4158 \) (from Statement I) 2. \( 2\pi r (r + h) = 1485 \) (from Statement II) - To find \( h \), we need to eliminate one variable. However, both equations contain two variables, and we cannot solve for \( h \) without knowing \( r \). 4. **Conclusion**: - Since we have two equations with two unknowns and no additional information to find the value of \( r \), we cannot determine the height \( h \) of the cylinder. - Therefore, the data given in both statements are not sufficient to answer the question. ### Final Answer: The answer is option 4: Both statement I and II together are not sufficient to answer the question.
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