Question

Find the surface area of a $$10cm \times 4cm \times 3cm$$ brick:
A) 84 square cm
B) 124 square cm
C) 164 square cm
D) 180 square cm

Answer 1

Hint:
Here brick means cuboid as their dimensions are the same, so we will need the formula for cuboid. Here we need to find the surface area of, so we have put given values in formula which is $$2 \times \left( {l \times b + b \times h + h \times l} \right)$$

Complete step by step solution:
We can say brick is a type of cuboid, so we will need a formula of surface area of cuboid.
The formula for calculating the surface area of a cuboid with dimensions $$l \times b \times h$$ is $$2 \times \left( {l \times b + b \times h + h \times l} \right)$$
Where $$l$$ is length, $$b$$ is breadth and $$h$$ is height
 In problem dimensions are given which are $$10cm \times 4cm \times 3cm$$
Substituting the values as

$$l = 10cm,b = 4cm,h = 3cm$$

Surface area =
$$\eqalign{
  & 2 \times \left( {l \times b + b \times h + h \times l} \right) \cr
  & = 2 \times \left( {10 \times 4 + 4 \times 3 + 3 \times 10} \right) \cr
  & = 2 \times \left( {40 + 12 + 30} \right) \cr
  & = 2 \times 82c{m^2} \cr
  & = 164c{m^2} \cr} $$

Hence answer is $$164c{m^2}$$ which option (C).

Note:
We already knew the formula for the surface area of the cuboid which is $$2 \times \left( {l \times b + b \times h + h \times l} \right)$$ . The dimensions were given as $$10cm \times 4cm \times 3cm$$ i.e. $$l = 10cm,b = 4cm,h = 3cm$$ . We put the correct values in the formula and then we got the answer.