Cylinder Volume Calculation
This problem asks for the volume of a cylinder given its radius and height.
Given Information
- Radius ($r$) = 28 cm
- Height ($h$) = 40 cm
- Value of Pi ($\pi$) $\approx \frac{22}{7}$
Volume Formula
The formula to calculate the volume ($V$) of a cylinder is:
$ V = \pi r^2 h $
Calculation Steps
- Substitute the given radius and height into the formula:
$ V = \frac{22}{7} \times (28 \text{ cm})^2 \times (40 \text{ cm}) $
- Calculate the square of the radius:
$ (28 \text{ cm})^2 = 28 \text{ cm} \times 28 \text{ cm} = 784 \text{ cm}^2 $
- Substitute this back into the volume equation:
$ V = \frac{22}{7} \times 784 \text{ cm}^2 \times 40 \text{ cm} $
- Simplify by dividing 784 by 7:
$ \frac{784}{7} = 112 $
$ V = 22 \times 112 \text{ cm}^2 \times 40 \text{ cm} $
- Multiply the remaining numbers:
$ V = 22 \times (112 \times 40) \text{ cm}^3 $
$ V = 22 \times 4480 \text{ cm}^3 $
- Calculate the final volume:
$ V = 98560 \text{ cm}^3 $
Conclusion
The calculated volume of the cylinder is 98560 $cm^3$.
Similar Questions
- The radius of a sphere is 16 cm. Find its surface area.
- What is the ratio of volumes of two spheres where the curved surface areas are in the ratio of $1 : 4$?
- Five solid cubes, each of volume $39304 \text{ cm}^3$, are joined end to end to form a cuboid. What is the lateral surface area (in $\text{cm}^2$) of the cuboid?
- What is the surface area of a sphere of radius 8 cm? (use $\pi = 3.14$)
- The ratio of the volumes of two cubes is 64 : 1331. What is the ratio of their total surface areas?
- The diameter of a hemisphere is 7 cm. What will its total surface area be?
- The diameters of the bases of two cones are equal. If their slant heights are in the ratio of 3 : 4, then what will the ratio of their curved surface areas be?
- A cube of volume 324 cm$^3$ is molded into a cuboid whose length, width and height are in the ratio $3 : 2 : 2$. Find the length of the cuboid.
- An aquarium is in the form of a cuboid whose external measures are $80 \text{ cm} \times 30 \text{ cm} \times 40 \text{ cm}$. The base, side faces and back face are to be covered with a coloured paper. Find the area of the paper needed?
- A godown is in the form of a cuboid of measures $60 \text{ m} \times 40 \text{ m} \times 30 \text{ m}$. How many cuboidal boxes can be stored in it if the volume of one box is $0.8 \text{ m}^3$?
Important Questions from 3-D Mensuration
Find the total surface area of a closed cylinder having a base radius of 70 m and a height of 110 m. [Use π = \(22\over7\)]
- The curved surface area of a cylinder is half of its total surface area. If its height is 195 cm, then find its diameter (in cm).
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(Use $\pi = \frac{22}{7}$)- A cylindrical rod has an curved surface area of $4,900 \text{ cm}^2$. If the length of the rod is 97 cm, then the radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$ - The volume (in $m^3$) of a cube, each of whose edges is 42 m, is:
