Cuboid Dimensions Ratio Explained
The problem states that the length, breadth, and height of a cuboid are in the ratio 5 : 4 : 3. We can represent these dimensions using a common multiplier, say x.
- Let the length = $5x$
- Let the breadth = $4x$
- Let the height = $3x$
Calculating Actual Cuboid Dimensions
We are given that the sum of the length, breadth, and height is 120 cm. Using the representations above:
$5x + 4x + 3x = 120 \text{ cm}$
Combine the terms:
$12x = 120 \text{ cm}$
Solve for x:
$x = \frac{120 \text{ cm}}{12} = 10 \text{ cm}$
Now, calculate the actual dimensions:
- Length = $5x = 5 \times 10 \text{ cm} = 50 \text{ cm}$
- Breadth = $4x = 4 \times 10 \text{ cm} = 40 \text{ cm}$
- Height = $3x = 3 \times 10 \text{ cm} = 30 \text{ cm}$
Cuboid Volume Calculation
The formula for the volume (V) of a cuboid is:
$V = \text{length} \times \text{breadth} \times \text{height}$
Substitute the calculated dimensions:
$V = 50 \text{ cm} \times 40 \text{ cm} \times 30 \text{ cm}$
Calculate the final volume:
$V = 2000 \text{ cm}^2 \times 30 \text{ cm}$
$V = 60,000 \text{ cm}^3$
Similar Questions
- The radius of a sphere is 16 cm. Find its surface area.
- The total surface area of a cube having side 40 cm is:
- A cuboid has length 10 cm, breadth 5 cm and height 2 cm. What is its surface area?
- The curve surface area of a cylindrical pillar is $264\text{ m}^2$ and its volume is $924\text{ m}^3$. Find the ratio of its height to its diameter.
- Find the total surface area of a cone, if its radius and slant height are $2r$ and $\frac{1}{2}$ respectively.
- If the surface area of a cube is $1014\text{ m}^{2}$, then its volume is:
- 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?
- Find the surface area of a sphere whose diameter is equal to 54 cm.
- What is the surface area of a sphere of radius 8 cm? (use $\pi = 3.14$)
- A cylinder and a cone have the same height and the same radius as that of their base. The ratio of the volume of the cone to the volume of the cylinder is:
Important Questions from 3-D Mensuration
- Find the surface area of a sphere whose diameter is equal to 98 cm.
- A conical vessel has base radius 31 cm and height 45 cm. Water is poured into the vessel until it is $\frac{2}{3}$ full. Find the volume (in cm³) of water in the vessel.
- A solid metallic sphere of radius 10 cm is melted and recast into 125 identical spheres. What is the ratio of the surface area of the original sphere to the total surface area of 6 smaller spheres so formed?
- Find the volume (in cm³) of the largest right circular cone that can be cut out from a cube with an edge of 8 cm. Use $\pi = \frac{22}{7}$
- The volume of a solid cylinder is 5852 cm³ and its height is 38 cm. What is the total surface area of the solid cylinder? (Round your answer to the nearest integer) (Use $\pi = \frac{22}{7}$)
