$1804 cm^2$
Cylinder Information
We are given the following details for a solid cylinder:
- Volume ($V$): $5,236 \text{ cm}^3$
- Height ($h$): $34 \text{ cm}
- Value of $\pi$: $\frac{22}{7}
Cylinder Radius Calculation
The formula for the volume ($V$) of a cylinder is $V = \pi r^2 h$. We use the given volume and height to find the radius ($r$).
Substitute the known values into the formula:
$ 5,236 = \frac{22}{7} \times r^2 \times 34 $Rearrange the equation to solve for $r^2$:
$ r^2 = \frac{5,236 \times 7}{22 \times 34} $ $ r^2 = \frac{36,652}{748} $ $ r^2 = 49 $Calculate the radius by taking the square root:
$ r = \sqrt{49} = 7 \text{ cm} $Total Surface Area Calculation
The formula for the total surface area (TSA) of a solid cylinder is $TSA = 2\pi r (r+h)$.
Substitute the calculated radius ($r = 7$ cm) and the given height ($h = 34$ cm) into the TSA formula:
$ TSA = 2 \times \frac{22}{7} \times 7 \times (7 + 34) $Simplify the expression:
$ TSA = 2 \times 22 \times (41) $ $ TSA = 44 \times 41 $ $ TSA = 1,804 \text{ cm}^2 $Final Answer
The total surface area of the solid cylinder is $1,804 \text{ cm}^2$.
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Important Questions from Mensuration
In a circular garden of radius 15 m, a path of 2 m wide has to be made inside the garden at the rate of ₹ 24 per sq. m. The cost of making the path is: (Take π = \(\frac{22}{7}\) )
A hollow cylinder with outer radius 4 cm and height 2 cm is made up of 1 cm thick metal sheet. What is the volume of metal used? (Take π = \(\frac{22}{7}\))
The sides of a triangular park are 60 m, 297 m and 303 m. Its area is equal to the area of a square-shaped garden. What is the perimeter (in m) of the garden?
The length and breadth of a rectangular field are in the ratio 4 : 3. If the cost of cultivating the field at ₹2 per m 2is ₹600, then the length of the field is:
A cylindrical tank has a capacity of 5632 m3. If the diameter of its base is 8 m, what is the depth of the cylindrical tank? (Use π = \(\frac{22}{7}\))
