Given Cylinder Information
- Lateral Surface Area ($LSA$): $140.1 \text{ cm}^2$
- Height ($h$): $3 \text{ cm}$
- Value of $\pi$: $3.14$
Finding Cylinder Radius
The formula for the lateral surface area of a cylinder is $LSA = 2 \pi r h$. Use the given values to find the radius ($r$).
- Substitute the known values into the $LSA$ formula:
$140.1 = 2 \times 3.14 \times r \times 3$
- Simplify the equation:
$140.1 = 18.84 \times r$
- Solve for $r$:
$r = \frac{140.1}{18.84}$
$r \approx 7.4363 \text{ cm}$
Calculating Cylinder Volume
The formula for the volume of a cylinder is $V = \pi r^2 h$. Use the calculated radius and the given height.
- Substitute the values of $\pi$, $r$, and $h$ into the volume formula:
$V = 3.14 \times (7.4363)^2 \times 3$
- Calculate the square of the radius:
$V = 3.14 \times 55.2985 \times 3$
- Calculate the final volume:
$V = 3.14 \times 165.8955$
$V \approx 520.9122 \text{ cm}^3$
- Round the volume to two decimal places:
$V \approx 520.91 \text{ cm}^3$
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 cylindrical rod has an outer curved surface area of \(7500 \text{ cm}^2\). If the length of the rod is 92 cm, then the outer radius (in cm) of the rod, rounded off to two places of decimal, is:
\(\left(\text{Take } \pi = \frac{22}{7}\right)\) - 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:
There is a wooden block in the form of a cube whose each side is 8 meters long.
The maximum possible number of cylinders with a diameter of 1 meter and a height of 4 meters were cut from this block. The cylinders are to be painted at the rate of ₹14 per square meter.
What is the total amount (in ₹) needed to paint all the cylinders if we paint the entire surface of each cylinder? (Take $\pi = \frac{22}{7}$)
- Six cubes each of side 4 cm, are placed adjacent to each other. Find the volume of the cuboid so formed.
