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xeze [42]
3 years ago
15

The solid surface area is equal to the solid volume. Find the value of x? The measurements of the rectangular prism is 9 inches

long and 4 inches wide. Height is not listed. socratic.org
Mathematics
1 answer:
Fudgin [204]3 years ago
6 0

Answer:

x=7.2

Step-by-step explanation:

Let x represent height of the prism.

We know that volume of rectangular is equal to product of its height, width and length.

\text{Surface area of rectangular prism}=2(wl+lh+hw), where w, h and l represents width, length and height respectively.

We have been given that the surface area of rectangular prism is equal to the volume of the prism. So we can set an equation as:

lwh=2(wl+lh+hw)

We are also told that the measurements of the rectangular prism is 9 inches long and 4 inches wide. Upon substituting these values in above equation, we will get:

9\cdot 4\cdot x=2(4\cdot  9+9\cdot x+x\cdot 4)

Let us solve for x.

36x=2(36+9x+4x)  

36x=2(36+13x)

36x=2(36+13x)

36x=72+26x

36x-26x=72+26x-26x

10x=72

x=\frac{72}{10}\\\\x=7.2

Therefore, the value of x is 7.2 inches.

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Answer:

(1) The required ratio of spirit to varnish is 1:3.

(2) You need 80 ml of mineral spirit.

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(1) If you need to mix 25% mineral spirit to the varnish, then the solution would contain 25% mineral spirit and 75% varnish.

So, \frac{spirit}{varnish}=\frac{25}{75}

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Thus, The required ratio of spirit to varnish is 1:3.

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Let x be the quantity of total solution.

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⇒\frac{240}{x}=\frac{3}{4}

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That is, total solution is 320 ml.

Now, Spirit = Total solution - Varnish

⇒Spirit = 320ml-240ml

⇒Spirit = 80ml

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Then, dimensions are 15m long and 10m wide.

Now, Height : Width = 15:10

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⇒\frac{Height}{Width} =\frac{3}{2}

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