The problem asks for the volume of a cylinder given its lateral surface area (LSA) and height.
Finding Cylinder Radius from LSA
We are given:
- Lateral Surface Area (LSA) = 775.8 cm$^2$
- Height (h) = 24 cm
- Value of $\pi = 3.14$
The formula for the Lateral Surface Area of a cylinder is:
LSA = $2 \pi r h$
We can use this formula to find the radius ($r$):
$775.8 = 2 \times 3.14 \times r \times 24$
$775.8 = 150.72 \times r$
Now, solve for $r$:
$r = \frac{775.8}{150.72}$
$r \approx 5.1473$ cm
Calculating Cylinder Volume
The formula for the Volume ($V$) of a cylinder is:
V = $\pi r^2 h$
Substitute the calculated radius ($r$) and the given height ($h$):
V = $3.14 \times (5.1473)^2 \times 24$
V = $3.14 \times 26.495 \times 24$
V = $3.14 \times 635.88$
V $\approx 1996.6332$ cm$^3$
Rounding the Volume
The question requires rounding the volume to two decimal places.
Volume $\approx 1996.63$ 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 $\pi = \frac{22}{7}$)
- Find the Total surface area of the hemisphere (in $cm^2$) whose radius is 26cm and $\pi = 3.14$.
