Question

Rukhsar painted the outside of the cabinet of measure\[1m \times 2m \times 1.5m\]. How much surface area did she cover if she painted all except the bottom of the cabinet?

Answer 1

Hint: The surface area of a solid is the sum of the areas of the plane or curved faces of the given solid, which is measured in square units such as square centi-meter \[{\left( {cm} \right)^2}\]and square meter \[{\left( m \right)^2}\]. The surface area of a cuboid is the sum of the surface areas of its six rectangular faces.
A cuboid is also known as rectangular cuboid is a three-dimensional shape having 6 faces and 12 edges, where the surface area of a side is equal to its opposite side, whose surface area is given as
\[SA = 2\left( {lb + lh + bh} \right)\]

Complete step-by-step answer:
To find the area of the surface, she painted to find the lateral surface area and the area of the top. To determine the surface area that Rukshar painted, we need to determine the total surface of the cabinet by using the formula as\[SA = \left\{ {2\left( {lb + lh + bh} \right)} \right\} - lb = lb + 2(lh + bh)\], this will give only the area of the surface which is painted.
According to the question, the dimension of the cabinet is \[1m \times 2m \times 1.5m\] for which,
Length \[l = 2m\], Breadth \[b = 1m\] and Height \[h = 1.5m\]
Since it has been already mentioned that the cabinet was not painted at the bottom, hence the surface area is needed to be found only for five faces, the top and the lateral surfaces.
The surface area of the top of the cabinet \[ = l \times b\]
Lateral surface area\[ = 2h\left( {l + b} \right)\]
So the surface area of cabinet= area of the top + lateral surface area
 \[
  SA = lb + 2h\left( {l + b} \right) \\
   = 2 \times 1 + 2\left( {1.5} \right)\left( {2 + 1} \right) \\
   = 2 + 3 \times 3 \\
   = 2 + 9 \\
   = 11{\text{ }}{m^2} \\
 \]
Hence, total surface area of the cabinet that was painted by Rukhsar is \[11{\text{ }}{m^2}\]

Note: Students can also find the surface area that Rukhsar painted by determining the total surface area first and then, subtract the area of the bottom as she did not paint the bottom of the cabinet.