\(\left(\text{Take } \pi = \frac{22}{7}\right)\)
Cylindrical Rod Surface Area Calculation
The problem asks for the outer radius of a cylindrical rod given its outer curved surface area and length.
Given Information:
- Outer Curved Surface Area = \(7500 \text{ cm}^2\)
- Length (Height, \(h\)) = \(92 \text{ cm}\)
- Value of \(\pi = \frac{22}{7}\)
Formula for Curved Surface Area of a Cylinder:
The formula for the curved surface area (CSA) of a cylinder is:
CSA = \(2 \pi r h\)
where \(r\) is the radius and \(h\) is the height (or length) of the cylinder.
Calculating the Radius:
- Substitute the given values into the formula:
\(7500 = 2 \times \frac{22}{7} \times r \times 92\)
- Simplify the equation:
\(7500 = \frac{44}{7} \times 92 \times r\)
\(7500 = \frac{4048}{7} \times r\)
- Isolate the radius (\(r\)):
\(r = \frac{7500 \times 7}{4048}\)
- Perform the calculation:
\(r = \frac{52500}{4048}\)
\(r \approx 12.969367... \text{ cm}\)
- Round the result to two decimal places:
\(r \approx 12.97 \text{ cm}\)
The outer radius of the rod is approximately 12.97 cm.
Similar Questions
- A number of 512 identical small spheres are cast from a sphere of radius 40 cm, with the total volume of the small spheres being equal to the volume of the larger sphere. The diameter (in cm) of each of the small spheres is:
- The radii of the internal and external surfaces of a hollow spherical shell are 6 cm and 4 cm respectively. If it is melted and recast into a solid cylinder of height $\frac{8}{3}$ cm, find the diameter of the cylinder.
- The diameter of a copper sphere is 12 cm. The sphere is melted and is drawn into a long wire of uniform circular cross - section. If the length of the wire is 48 cm, find its diameter.
- A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter $l$ cm of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Important Questions from Mensuration 3D (Notes)
- The height of a cylinder is 14cm and its curved surface area is 264cm². The volume of the cyclinder (in cm³) is:
($\pi=\frac{22}{7}$) - A number of 512 identical small spheres are cast from a sphere of radius 40 cm, with the total volume of the small spheres being equal to the volume of the larger sphere. The diameter (in cm) of each of the small spheres is:
- If the lateral surface area of a cylinder is 775.8 cm$^2$ and its height is 24 cm, then find its volume. (Use $\pi = 3.14$ and round off to two decimal places.)
- Find the Total surface area of the hemisphere (in $cm^2$) whose radius is 26cm and $\pi = 3.14$.
- Find the Total surface area of the hemisphere (in $cm^2$) whose radius is $48cm$ and $\pi = 3.14$.
