One cylinder has a volume that is 8cm less than 7/8 of the volume of a second cylinder. If the first cylinder’s volume is 216cm³, what is the correct equation and value of x, the volume of the second cylinder?

Equation: [tex]216 = \frac{7}{8} \cdot x - 8 [/tex]

To solve the equation, first multiply by 8:

[tex]216 \cdot 8 = 8\cdot \dfrac{7}{8} x - 8 \cdot 8[/tex]

[tex]1728 = 7 x - 64[/tex]

Add 64 to both members of the equation:

[tex]1728 + 64 = 7x - 64 + 64[/tex]

[tex]1792 = 7x[/tex]

And, finally, divide by 7 to get x:

[tex] \dfrac{1792}{7} = \dfrac{7x}{7}[/tex]

[tex]256 = x[/tex]

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ap8997154 ap8997154 · Answer 2 · 2022-05-03T14:29:16+02:00

A cylinder is a three-dimensional object. The volume of the second cylinder is 256 cm³.

What is a cylinder?

A cylinder is a three-dimensional object. The object can be assumed as a pile of circles kept over one another.

As it is given that the volume of the first cylinder is 216 cm³. Also, it is mentioned that the volume of the first cylinder is 8cm less than 7/8 of the volume of a second cylinder. Therefore, the equation for the volume of the two-cylinder can be written as,

[tex]\rm \text{(Volume of the first cylinder)} = \dfrac78\text{(Volume of the second cylinder)} - 8\ cm^3[/tex]

[tex]\rm \text{(Volume of the first cylinder)} = \dfrac78\text{(Volume of the second cylinder)} - 8\ cm^3\\V_1 = (\dfrac78 \times V_2) - 8\ cm^3\\[/tex]

Now, substitute the volume of the first cylinder,

[tex]V_1 = (\dfrac78 \times V_2) - 8\ cm^3\\\\216 = (\dfrac78 \times V_2)-8\\\\216+8 = (\dfrac78 \times V_2)\\\\224 = (\dfrac78 \times V_2)\\\\V_2 = \dfrac{224 \times 8}{7}\\\\V_2 = 256\ cm^3[/tex]

Hence, the volume of the second cylinder is 256 cm³.

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