Question

The volume of a cuboid is 6400 cu cm.its length is 32cm,and breadth and height are in the ration 2 : 1. Find its breadth and height​

Answer 1

Given :

• Volume of Cuboid = 6400 cm³
• Length = 32 cm
• Breadth and Height = 2:1

To Find :

• Breadth and Height = ?

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Volume {\small_{(Cuboid)}} = Length \times Width \times Height }}}}}$

$\dag$ Let the Ratios :

• Breadth = 2y
• Height = 1y

$\dag$ Calculating the Value of y :

${\dashrightarrow{\qquad{\sf{ Volume = Length \times Width \times Height }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 6400 = 32 \times 2y \times 1y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 6400 = 32 \times 2y^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \dfrac{6400}{32} = 2y^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{6400}{32} = 2y^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 200 = 2y^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \dfrac{200}{2} = y^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{200}{2} = y^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 100 = y^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \sqrt{100} = y }}}} \\ \\ \\ \ {\qquad \; \; {\dashrightarrow \; {\pmb{\underline{\boxed{\purple{\frak{ y = 10 }}}}}}}}$

$\dag$ Calculating the Breadth and Height :

• Breadth = 2y = 2(10) = 20 cm
• Height = 1y = 1(10) = 10 cm

$\therefore \;$ Breadth of the Cuboid is 20 cm and its Height is 10 cm .

$\\ \qquad{\rule{200pt}{2pt}}$

Answer 2

Answer:

The breadth of cuboid=20cm

Height of cuboid=10cm

Step-by-step explanation:

Question:-

The volume of a cuboid is 6400 cu cm.its length is 32cm,and breadth and height are in the ration 2 : 1. Find its breadth and height

Given:-

The volume of a cuboid is 6400cm^3

The cuboid's length is 32cm

To find:-

The breadth and height of cuboid whose ratio=2:1

Solution:-

Let us assume that,

Breadth=2x

Height=1x

According to the question

Volume of cuboid=length×breadth×height

On substituting the given values we get,

$6400 = 32 \times 2x \times 1x$

$6400 = 32 \times 2 {x}^{2}$

$\frac{6400}{32} = 2 {x}^{2}$

$200 = 2 {x}^{2}$

$\frac{200}{2} = {x}^{2}$

$100 = {x}^{2}$

$\sqrt{100} = x$

$10 = x$

Calculating the breadth and height of cuboid,

Breadth=2x=2(10) =20cm

Height=1x=1(10) =10cm

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