Problem Understanding
The question asks for the total volume of a cuboid formed by combining six identical cubes, each with a side length of 4 cm. These cubes are placed adjacent to each other.
Calculating Cuboid Volume
The most straightforward method to find the volume of the resulting cuboid is to sum the volumes of the individual cubes. This approach is independent of how the cubes are arranged.
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Volume of a Single Cube:
The formula for the volume of a cube is $V_{\text{cube}} = s^3$, where $s$ represents the side length.
Given the side length $s = 4$ cm, the volume of one cube is calculated as:
$ V_{\text{cube}} = (4 \text{ cm})^3 $ $ V_{\text{cube}} = 4 \times 4 \times 4 \text{ cm}^3 $ $ V_{\text{cuboid}} = 64 \text{ cm}^3 $
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Total Volume of the Cuboid:
Since there are 6 identical cubes, the total volume ($V_{\text{total}}$) of the cuboid formed is 6 times the volume of a single cube.
$ V_{\text{total}} = \text{Number of cubes} \times V_{\text{cube}} $ $ V_{\text{total}} = 6 \times 64 \text{ cm}^3 $ $ V_{\text{total}} = 384 \text{ cm}^3 $
Final Answer
The volume of the cuboid formed by placing six adjacent cubes, each with a side length of 4 cm, is 384 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 $\pi = \frac{22}{7}$)
- If the lateral surface area of a cylinder is $140.1 \text{ cm}^2$ and its height is $3 \text{ cm}$, then find its volume. (Use $\pi = 3.14$ and round off to two decimal places.)
