If 2/3 = x/12, what is the value of x? A)4. B)8. C)18. D)24.

Mathematics

1 answer:

Vikki [24]3 years ago

7 0

B because of what is shown above.

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Hello,how do I calculate the the volume of this compound shape?

Setler [38]

To calculate the volume, we can divide this figure into three shapes. Three rectangular prisms, like the following image

The volume of a rectangular prism is given by the product between its 3 different dimensions, width, length and height. The green prism is the easiest to see the its dimensions, it has a width equals to 3, a length equals to 3 and a height equal to 1/2, therefore, its volume is

$V_g=3\times3\times\frac{1}{2}=9\times\frac{1}{2}=\frac{9}{2}=4\frac{1}{2}$

Since the width of the green prism is 3 and the red prism is 1 1/2 apart from the corner of the green prism, the width of the red prism is the difference between those values.

$3-1\frac{1}{2}=\frac{6}{2}-\frac{3}{2}=\frac{6-3}{2}=\frac{3}{2}=1\frac{1}{2}$

The length and the height of the red prism are also easy to see on the image, both of those values are 1, which means the volume of the red prism is

$V_r=1\frac{1}{2}\times1\times1=1\frac{1}{2}$

Finally, the last prism is the blue prism. The height of the green prism and the blue prism combined is equal to 3/4. Since the height of the green prism is 1/2, the height of the blue prism is