Question

The volume of a rectangular prism is 2058 cm3. The length is three times the
width. The height is twice the width. Find the width, length and height of the
prism.​

Answer 1

Answer:

Let the height of prism be

H

.

As it is twice the width, width is

H

2

.

Length being

3

times width should be

3

×

H

2

=

3

H

2

Hence, volume is

3

H

2

×

H

×

H

2

=

3

4

H

3

, but it is

2058

cubic cm.

Therefore

3

4

H

3

=

2058

and

H

3

=

2058

×

4

3

=

686

2058

×

4

1

3

or

H

3

=

2

×

2

×

2

×

7

×

7

×

7

Hence

H

=

2

×

7

=

14

Height of the prism is

14

cm.it is twice the width, width is H2 . Hence, volume is 3H2×H×H2=34H3 , but it is 2058 cubic cm.

Answer 2

• Width of the rectangular prism = 7 cm

• = 7 cmLength of the rectangular prism = 21 cm

• = 7 cmLength of the rectangular prism = 21 cmHeight of the rectangular prism = 14 cm

Given :

• The volume of a rectangular prism is 2058 cm³

• The length is three times the width

• The height is twice the width

To find :

The width , length and height of the prism

Formula Used :

Volume of a rectangular prism

= Length × Width × Height

Solution :

Step 1 of 2 :

Form the equation to calculate width , length and height of the prism

Let width of the rectangular prism = w cm

Since length is three times the width

∴ Length of the rectangular prism = 3w cm

Since height is twice the width

∴ Height of the rectangular prism = 2w cm

∴ Volume of the rectangular prism

= Length × Width × Height

= (3w × w × 2w) cm³

= 6w³ cm³

By the given condition

$\displaystyle \sf 6 {w}^{3} = 2058$

Step 2 of 2 :

Calculate width , length and height of the prism

$\displaystyle \sf 6 {w}^{3} = 2058$

$\displaystyle \sf{ \implies }{w}^{3} = \frac{2058}{6}$

$\displaystyle \sf{ \implies }{w}^{3} = 343$

$\displaystyle \sf{ \implies }{w}^{3} = {7}^{3}$

$\displaystyle \sf{ \implies }w = 7$

Width of the rectangular prism

= w cm

= 7 cm

Length of the rectangular prism

= 3w cm

= (3 × 7) cm

= 21 cm

Height of the rectangular prism

= 2w cm

= (2 × 7) cm

= 14 cm

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