Question

The length, breadth and height of a cuboid are in the ratio 7:6:5 . If the surface area of the cuboid is
1962cm², find it's dimensions. Also find the volume of the cuboid.​

Answer 1

$\large \boxed{ǫᴜᴇsᴛɪᴏɴ}$

The length, breadth and height of a cuboid are in the ratio 7:6:5 . If the surface area of the cuboid is 1926cm², find it's dimensions. Also find the volume of the cuboid.

Given:-

Surface area of a cuboid = 1926cm²

Ratio of dimensions = 7:6:5

Let,

The length of the cuboid be 7x

The breadth of a cuboid be 6x

The height of a cuboid be 5x

We know,

$\small\tt\boxed{Surface~area~ of ~a~ cuboid= 2(lb+lh+bh)}$

From Question,

Surface area of cuboid = 1926

2(lb+lh+bh) = 1926

=>2[7x•6x+7x•5x+6x•5x] = 1926

=>2[42x+35x+30x] = 1926

=> 2(107x). = 1926

=> 214x = 1926

=> x = $\frac{1926}{214}$

=> x = 9

Therefore, substituting the value of x

Length = 7 × 9 = 63cm

Breadth = 6 × 9 = 54cm

Height = 5 × 9 = 45cm

We have,

$\small\tt \boxed{Volume ~of ~a~ cuboid = l×b×height}$

Volume= 63×54×45

= 153090cm³

$\tt\small \boxed{ғɪɴᴀʟ~ᴀɴsᴡᴇʀ}$

Length = 7 × 9 = 63cm

Breadth = 6 × 9 = 54cm

Height = 5 × 9 = 45cm

Volume= 153090cm³

Answer 2

${\huge{\underbrace{\frak{Question:-}}}}$

The Length , Breadth & Height of a Cuboid are in the ratio 7:6:5 . If the surface area of the Cuboid is 1926 cm² , find it's dimensions . Also find the volume of the Cuboid .

${\huge{\underbrace{\frak{Solution\checkmark}}}}$

$\frak{Given}\begin{cases}\sf{Given\;Figure\;is\;a\; \bf{Cuboid}}\\ \sf{Length:Breadth:Height=\bf{7:6:5}}\\ \sf{Total\;Surface\;Area=\bf{1926\;cm^2}}\end{cases}$

$\frak{To\;Find}\begin{cases}\sf{The\; Dimensions\;of\;the\;Cuboid}\\ \sf{Volume}\end{cases}$

${\large{\underline{\textit{\textbf{Answer:–}}}}}$

Let the ratios of 7x , 6x & 5x .

So ,

• Length (l) = 7x
• Breadth (b) = 6x
• Height (h) = 5x

Now ,

Using the Formula for finding TSA

$\pink \star \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \sf{tsa = 2(lb + bh + lh)}}$

$\rightarrow \rm \: 1926 \: {cm}^{2} = 2(7x \times 6x + 6x \times 5x + 5x \times 7x)$

$\rightarrow \rm \: 1926 \: {cm}^{2} = 2(42x^2 + 30x^2 + 35x^2)$

$\rightarrow \rm \: \cancel{1926}\: {cm}^{2} = \cancel2 \times \cancel{107}x^2$

$\rightarrow \rm \: {x}^{2} = 9 \: {cm}^{2}$

$\rightarrow \: \: \: \: \: \: \: \: \: \boxed{ \rm{x = 3 \: cm}}$

So ,

$\bull \rm \: length = 7x = 7 \times 3 \: cm \\ \underline{ \boxed{ \rm{ \pink{length = 21 \: cm}}}}$

$\bull \rm \: breadth = 6x = 6 \times 3 \: cm \\ \underline{ \boxed{ \rm{ \green{breadth = 18 \: cm}}}}$

$\bull \rm \: height = 5x = 5 \times 3 \: cm \\ \underline{ \boxed{ \rm{ \purple{height = 15 \: cm}}}}$

★ Dimensions : 21cm × 18cm × 15cm .

${\underline{\bf{\bigstar\; Finding\;Volume}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \sf{volume = lbh}}$

$\mapsto \rm \: volume = 21 \: cm \times 18 \: cm \times 15 \: cm$

$\mapsto \: \: \: \: \: \: \underline{ \boxed{ \rm{ \blue{volume = 5670 \: {cm}^{3}}}}}$

★ Volume of the Cuboid = 5670 cm³ .