Question

The length, breadth and height of a cuboid are in the ratio 7 : 4 : 3 respectively.
If the whole surface area of the cuboid is 1098 cm2, find its dimensions.
Also, find its volume.

Answer 1

Given :

• The length, breadth and height of a cuboid are in the ratio 7 : 4 : 3.
• Total surface area → 1098 cm²

To Find :

• Dimension of the cuboid.
• Volume of the cubical.

Solution :

Let x be the common of the ratio given.

•°• Length → 7x

Breadth → 4x

Height → 3x

Given, total surface area → 1098.

So, let's use the formula of total surface area of the cuboid.

Formula :

$\large{\red{\boxed{\mathtt{TSA_{cuboid}\:=\:2\:(lb\:+bh\:+hl)}}}}$

Block in the values,

$\mathtt{1098=2(7x\:\times\:4x\:+\:4x\:\times\:3x\:+\:3x\:\times\:7x}$

➣ $\mathtt{1098=2(28x^2+12x^2+21x^2)}$

➣ $\mathtt{1098=2(61x^2)}$

➣ $\mathtt{1098=122x^2}$

➣ $\mathtt{\dfrac{1098}{122}=x^2}$

➣ $\mathtt{9=x^2}$

➣ $\mathtt{\sqrt{9}=x}$

➣ $\mathtt{3=x}$

Substitute, x = 3 in the values of the assumed ratio.

Length :

• 7x = 7 × 3 = 21 cm.

Breadth :

• 4x = 4 × 3 = 12 cm

Height :

• 3x = 3 × 3 = 9 cm.

Now, we have the dimensions of cuboid.

Using these in the formula of volume of cuboid, we can calculate the volume.

Formula :

$\large{\red{\boxed{\mathtt{Volume_{cuboid}\:=\:l\:\times\:b\:\times\:h}}}}$

Where,

• l = length → 21 cm
• b = breath → 12 cm
• h = height → 9 cm

➣ $\mathtt{Volume_{Cuboid}\:=\:21\:\times\:12\:\times\:9}$

➣ $\mathtt{Volume_{Cuboid}\:=\:252 \:\times\:9}$

➣ $\mathtt{Volume_{Cuboid}\:=\:2268}$

$\large{\boxed{\mathtt{\red{Volume\:of\:cuboid\:=\:2268\:cm^3}}}}$