Question

The total sum of the perimeter of all the faces of cuboid is 176 cm. the length of its diagonal is 12 cm. Find the surface area of the cuboid

Answer 1

answer is 48. I think it will be satisfied.

Answer 2

Given,

For a cuboid;

The total sum of the perimeter of all the faces of cuboid = 176 cm

Length of its diagonal = 12 cm

To find,

The total surface area of the cuboid.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the dimensions of the cuboid are as follow;

Length of the cuboid = L cm

Breadth = B cm

Height = H cm

As per mensuration,

For any cuboid with length L units, breadth B units, and the height H units;

The total sum of the perimeter of all the faces of the cuboid = 4(L + B+ H)

Length of its diagonal = √(L^2 + B^2 + H^2)

The total surface area of the cuboid = 2(LB + BH + LH)

Now, according to the question;

The total sum of the perimeter of all the faces of cuboid = 176 cm

=> 4(L + B+ H) = 176 cm

=> (L + B+ H) = 44 cm {Equation-1}

Now,

Length of the diagonal of the cuboid = 12 cm

=> √(L^2 + B^2 + H^2) = 12 cm

=> L^2 + B^2 + H^2 = 144 sq. cm {Equation-2}

Now, on squaring the both sides of the equation-1, we get;

(L + B+ H)^2 = (44)^2 cm

=> L^2 + B^2 + H^2 + 2(LB + BH + LH) = 1936 sq. cm.

=> 2(LB + BH + LH) = 1936 sq. cm. - (L^2 + B^2 + H^2) = 1936 sq. cm - 144 sq. cm

{According to equation-2}

=> 2(LB + BH + LH) = 1792 sq. cm

=> Total surface area of the cuboid = 1792 sq. cm

Hence, the total surface area of the cuboid is equal to 1792 sq. cm.