Question

please answer these two questions with explanation #EXPERT #GENIUS​​

Answer 1

1)Question:-

The curved surface area of a cylinder is 2π (y²-7y + 12) and its radius is (y-3). Find the height of the cylinder.

Answer:-

Given:

• CSA=2π (y²-7y + 12)
• Radius=y-3

To find:

• Height of cylinder.

Solution:

We know:

$\leadsto \underline{\boxed{\sf CSA\ of\ cylinder = 2\pi rh}}$

Putting values,

$\displaystyle :\implies \sf 2\pi (y^2 +7y+12)=2\pi (y-3)h\\\\:\implies \sf h = \frac{\cancel{2\pi}(y^2 +7y+12)}{\cancel{2\pi}(y-3)} \\\\:\implies \sf h = \frac{y^2 -4y-3y+12}{y-3} \\\\:\implies \sf h=\frac{y(y-4)-3(y-4)}{y-3} \\\\:\implies \sf h = \frac{\cancel{(y-3)}(y-4)}{\cancel{y-3}} \\\\:\implies \boxed{\boxed{\sf h = y-4}}$

Hence,

The height of cylinder is y-4

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2)Question:-

The area of a rectangle is x²+ 7x + 12. If its breadth is (x + 3), then find its length.

Answer :-

Given:

• Area of rectangle = x²+ 7x + 12
• Breadth = x+3

To find:

• Length

Solution:

Using the formula,

$\leadsto \underline{\boxed{\sf Area = length \times breadth }}$

Putting the values,

$\displaystyle :\implies \sf x^2 +7x + 12 =length\times (x+3)\\\\\\:\implies \sf length = \frac{x^2 + 7x +12}{x+3} \\\\\\:\implies \sf length= \frac{x^2 + 4x +3x +12 }{x+3} \\\\\\:\implies \sf length = \frac{x(x+4)+3(x+4)}{x+3} \\\\\\:\implies \sf length = \frac{(x+4)\cancel{(x+3)}}{\cancel{(x+3)}}\\\\\\:\implies \boxed{\boxed{\sf length = x+3 }}$

Hence,

The length of rectangle is x+3.

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