Question

Cuboid shaped bar 6 cm long, 5 cm wide and 2 cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain the same, but the length and width will be decreased by the same percentage. The new width will be. ​

Answer 1

ᴠᴏʟᴜᴍᴇ=ʟ×ʙ×ʜ=6×5×2=60ᴄᴍ

3

ᴅᴇᴄʀᴇᴀsᴇ ɪɴ ᴠᴏʟᴜᴍᴇ=20%

∴ɴᴇᴡ ᴠᴏʟᴜᴍᴇ=80% ᴏғ 60=48ᴄᴍ

3

ʟᴇᴛ ʟᴇɴɢᴛʜ ᴅᴇᴄʀᴇᴀsᴇ ʙʏ x% ᴡʜɪᴄʜ ɪs ᴀʟsᴏ ɪɴ ʙʀᴇᴀᴅᴛʜ

ɴᴏᴡ, ɴᴇᴡ ᴠᴏʟᴜᴍᴇ=(6−

100

6x

)×(5−

100

5x

)×2

⇒

2

48

=30−

100

30x

−

100

30x

+

10000

30x

2

⇒24=30−

100

60x

+

10000

30x

2

⇒

10000

30x

2

−

100

60x

+30−24=0

⇒

10000

30x

2

−

100

60x

+6=0

⇒30x

2

−6000x+60000=0

⇒x

2

−200x+2000=0

x=100−40

5

& 100+40

5

∴x=100−40

5

=100−89.44=10.56 & x=100+89.44=189.44

∴ʟ=6−

100

6×10.56

=6−0.6=5.4

∴5<ʟ<5.5

Answer 2

The new width is 4.5cm.

Given:

Cuboid-shaped bar that is 6 cm long, 5 cm wide, and 2 cm thick.

To Find:

The new width after the volume of the bar has been reduced by 19%.

Solution:

The initial length, width, and thickness of the cuboid are 6 cm, 5 cm, and 2 cm respectively.

Hence the initial volume of the cuboid = length x width x thickness

⇒ Initial volume of the cuboid = 6 x 5 x 2 = 60 $cm^{3}$

Now to cut costs, the company had decided to reduce the volume of the bar by 19%.

So new volume = 60 - ($\frac{19}{100}$ x 60) = 48.6

The new thickness remains same= 2cm.

It is given that the new length and width decreases by the same percentage, say by x%.

⇒ New length = (6 - $\frac{6x}{100}$ ) cm

New width = (5 - $\frac{5x}{100}$) cm

∴ New volume =  (6 - $\frac{6x}{100}$ ) x  (5 - $\frac{5x}{100}$) x 2

⇒ 48.6 x 10000 = (600-6$x$)(500-5$x$)(2)

⇒ 8100 = $(100-x)^{2}$

⇒ $x^{2}$ - 200$x$ + 1900 = 0

 Solving this quadratic equation we obtain the possible value of x = 10

⇒ New width = (5 - $\frac{5* 10}{100}$) = $\frac{9}{2}$ = 4.5cm

∴ The new width is 4.5cm.

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