The length, breadth and height of a cuboid are 4 cm, 6 cm and 10 cm respectively. Find the total surface area.
248 cm2
Calculating Total Surface Area of a Cuboid
The problem asks us to find the total surface area of a cuboid given its dimensions: length, breadth, and height.
Understanding Cuboid Dimensions
A cuboid is a three-dimensional shape with six rectangular faces. The dimensions given are:
- Length (l) = 4 cm
- Breadth (b) = 6 cm
- Height (h) = 10 cm
Formula for Total Surface Area of a Cuboid
The total surface area of a cuboid is the sum of the areas of all six faces. Since opposite faces are identical, the formula is derived by adding the areas of the three unique pairs of faces:
Area of front and back faces = $2 \times (length \times height) = 2lh$
Area of top and bottom faces = $2 \times (length \times breadth) = 2lb$
Area of left and right faces = $2 \times (breadth \times height) = 2bh$
Total Surface Area (TSA) = Area of front/back + Area of top/bottom + Area of left/right
The formula for the total surface area (TSA) of a cuboid is:
TSA = $2(lb + bh + hl)$
Step-by-Step Calculation of Total Surface Area
Now, let's substitute the given dimensions into the formula:
- Length (l) = 4 cm
- Breadth (b) = 6 cm
- Height (h) = 10 cm
TSA = $2 \times ((4 \text{ cm} \times 6 \text{ cm}) + (6 \text{ cm} \times 10 \text{ cm}) + (10 \text{ cm} \times 4 \text{ cm}))$
First, calculate the area of each pair of faces:
- $l \times b = 4 \text{ cm} \times 6 \text{ cm} = 24 \text{ cm}^2$
- $b \times h = 6 \text{ cm} \times 10 \text{ cm} = 60 \text{ cm}^2$
- $h \times l = 10 \text{ cm} \times 4 \text{ cm} = 40 \text{ cm}^2$
Next, sum these areas:
$lb + bh + hl = 24 \text{ cm}^2 + 60 \text{ cm}^2 + 40 \text{ cm}^2 = 124 \text{ cm}^2$
Finally, multiply the sum by 2 to get the total surface area:
TSA = $2 \times 124 \text{ cm}^2 = 248 \text{ cm}^2$
Final Answer Confirmation
The total surface area of the cuboid with length 4 cm, breadth 6 cm, and height 10 cm is 248 cm2.
Revision Table: Cuboid Properties
| Property | Formula | Description |
|---|---|---|
| Volume | $V = l \times b \times h$ | Space occupied by the cuboid |
| Lateral Surface Area | $LSA = 2h(l + b)$ | Area of the four side faces (excluding top and bottom) |
| Total Surface Area | $TSA = 2(lb + bh + hl)$ | Area of all six faces |
| Diagonal of Cuboid | $d = \sqrt{l^2 + b^2 + h^2}$ | Length of the longest diagonal inside the cuboid |
Additional Information: Understanding Surface Area
Surface area is a measure of the total area that the surface of a three-dimensional object occupies. For a cuboid, it's like unfolding the box and finding the total area of the resulting 2D shape (net). Calculating surface area is important in various real-world applications, such as determining the amount of paint needed to cover a wall, the material required to wrap a gift, or the amount of heat that can be radiated or absorbed by an object.
The units for surface area are always square units (e.g., cm2, m2, in2) because it represents an area.
Important Questions from Solid Figures
- Find the volume of the cylinder whose radius is 38.5 cm and height is 18 cm. (use $\pi = 22/7$ and In $cm^3$)
- Find the surface area of the sphere (in $cm^2$) whose radius is 168 cm and $\pi = 22/7$.
- Find the volume of the cylinder whose radius is 21 cm and height is 13 cm. (In $cm^3$ and use $\pi = 22/7$)
- A solid spherical ball made of iron is melted and two new balls are made whose diameters are in the ratio of 1:2. The ratio of the volume of the smaller new ball to the original ball is
If a cubical container of length, breadth and height each of 10 cm can contain exactly 1 litre of water, then a spherical container of radius 10.5 cm can contain
