Question

The surface area of a cuboid is 4212 m. If its dimensions are in the ratio 4:3:2, then
find the volume of the cuboid.

Answer 1

Answer:

Hint: First we will define what is meant by cuboid then we will assume a variable for the length breadth and the height of the cuboid and then we will apply the formula for the total surface area of a cuboid that is 2(lb+bh+hl) then we will get the dimensions of the cuboid. Then for finding the volume of the cuboid we will apply the formula: (length×breadth×height)and get the answer.

Complete step by step answer:

Let’s first see what is meant by a cuboid. So, A cuboid is a three dimensional shape having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel. But not all the faces of a cuboid are equal in dimensions.

Now let the length, breadth and height of the cuboid be 4x,3x and 2x.

Given that the surface area of the cuboid is 4212 m2.

We know that the surface area of a cuboid of length l , breadth b and height h is 2(lb+bh+hl)

Now, we will put the values given in the question to find out the surface area of cuboid:

⇒4212=2((4x.3x)+(3x.2x)+(2x.4x))⇒2106=(12x2+6x2+8x2)⇒2106=26x2⇒x2=81

Taking square roots on both the sides, we will get: ⇒x=±9 , since dimension cannot be negative therefore: x=9

Now, the length of the cuboid will be 4x=4×9=36 m , breadth will be 3x=3×9=27 m and height 2x=2×9=18 m

Now, we know that the volume of the cuboid is (length×breadth×height)

Therefore, the volume of the given cuboid will be: (36×27×18)=17496 m3

Hence, the answer is 17496 m3 .

Note: Common mistake can be made while applying the total surface area formula and instead of that one can use the lateral surface area formula that is 2h(l+b), this will lead to a totally different answer. Also, units must be mentioned at every step