If the dimensions of a cuboid are 3cm, 4cm and 10cm, then its surface area is

Question

Accepted Answer

The correct option is 3:
To find the surface area of a cuboid, we use the formula for the total surface area (TSA) of a cuboid, which is given by:
$TSA = 2(lw + wh + lh)$
where $l$ is the length, $w$ is the width, and $h$ is the height of the cuboid.

Given dimensions are:
Length ($l$) = 3 cm
Width ($w$) = 4 cm
Height ($h$) = 10 cm

Now, substitute these values into the formula:
$TSA = 2((3 	ext{ cm} 	imes 4 	ext{ cm}) + (4 	ext{ cm} 	imes 10 	ext{ cm}) + (3 	ext{ cm} 	imes 10 	ext{ cm}))$
$TSA = 2(12 	ext{ cm}^2 + 40 	ext{ cm}^2 + 30 	ext{ cm}^2)$
$TSA = 2(82 	ext{ cm}^2)$
$TSA = 164 	ext{ cm}^2$
The calculated surface area is $164 	ext{ cm}^2$, which matches Option 3.

The incorrect option is 1:
$82 	ext{ cm}^2$ is incorrect. This value is half of the actual total surface area. It could be a result of not multiplying the sum of the areas of the three unique faces by 2.

The incorrect option is 2:
$123 	ext{ cm}^2$ is incorrect. This value does not correspond to the correct application of the surface area formula for the given dimensions. There might be an error in calculation or a misunderstanding of the formula.

The incorrect option is 4:
$216 	ext{ cm}^2$ is incorrect. This value is significantly higher than the correct surface area and would result from incorrect calculations or using an inappropriate formula. For example, it might arise from incorrect multiplication or addition.