Question

15. The volume of a cuboid is 750 cu. m If the length, breadth and height are in the ratio 3.221
in then find them.​

Answer 1

Answer:

total surface area is 504cm

2

The length, breadth, and height of a cuboid are in the ratio 6:5:3

total surface area =2(lb+bh+lh)

504 = 2(30x

2

+15x

2

+18x

2

)

504 = 2 x 63x

2

504 = 126x

2

x

2

=

126

504

= 4

∴x=2cm

Therefore,length= 6x=6x2 = 12cm

breadth = 5x =5(2) =10cm

height = 3x=3(2)=6cm

Volume of cuboid = area of the base x height = l×b×h = 12 x 10 x 6 = 720cm

3

Answer 2

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$\red\bigstar {\underline{\underline{\textbf{\textsf{Question :-}}}}}$

• The volume of a cuboid is 750m³ If the length, breadth and height are in the ratio 3.2:1 Then find them.

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$\red\bigstar {\underline{\underline{\textbf{\textsf{Given That :-}}}}}$

• The volume of the cuboid is 750m³
• The ratio of its dimensions are 3:2:1

$\red\bigstar {\underline{\underline{\textbf{\textsf{To Find :-}}}}}$

• The dimensions of the cuboid

$\red\bigstar {\underline{\underline{\textbf{\textsf{Assumptions :-}}}}}$

• Let the length of the cuboid be 3x
• Let the breadth of the cuboid be 3x
• Let the height of the cuboid be x

$\red\bigstar {\underline{\underline{\textbf{\textsf{ Formula Used :-}}}}}$

• Volume of a cuboid = l × b × h

$\red\bigstar {\underline{\underline{\textbf{\textsf{Where :-}}}}}$

• L stands for length
• B stands for breadth
• H stands for height

$\red\bigstar {\underline{\underline{\textbf{\textsf{Substituting The Values :-}}}}}$

$\leadsto \tt \qquad 3x \times 2x \times x = 750m^3$

$\leadsto \tt \qquad 6x^2 \times x = 750m^3$

$\leadsto \tt \qquad 6x^3 = 750m^3$

$\red\bigstar {\underline{\underline{\textbf{\textsf{By Dividing :-}}}}}$

$\leadsto \tt \qquad x^3 = \cancel\dfrac{750m^3}{6}$

$\leadsto \tt \qquad x^3 = 125m^3$

$\leadsto \tt \qquad x = \sqrt[3]{\tt 125m^3}$

$\leadsto \tt \qquad {\pink{\boxed{\frak{x = 5m}}}\purple\bigstar}$

$\red\bigstar {\underline{\underline{\textbf{\textsf{Therefore,}}}}}$

• Length = 3x = 3(5m) = 15m
• Breadth = 2x = 2(5m) = 10m
• Height = 1x = 1(5m) = 5m

ㅤㅤㅤㅤㅤㅤ━━━━━━━━━━

$\therefore {\underline{\sf{ Hence, the\; dimensions\; are\; 15m, 10m\;and \;5m \;respectively}}}$

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