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Mathematics

Grade10

Easy

Question

Find and simplify the ratio of the volume of Figure A to the volume of Figure B.

$\frac{(3 x + 3)}{(2 x + 4)}$
$\frac{(3 x + 7)}{(2 x + 4)}$
$\frac{(3 x)}{(2 x + 4)}$
$\frac{(4 x)}{(2 x + 3)}$

hint Hint:

In this question, we have to find the ratio of the volume of Figure A and figure B. If the dimension of Figure A are 3x, x, (x + 1) and the dimension of figure B are (x + 2), x, 2x.

The correct answer is: $fraction numerator left parenthesis 3 straight x space plus space 3 right parenthesis over denominator left parenthesis 2 straight x space plus space 4 right parenthesis end fraction$

Volume of figure A = length . breadth . height = 3x . x .(x + 1)
Volume of figure B = length . breadth . height = (x + 2) . x. 2x
$Ratio space equals space straight V subscript straight A over straight V subscript straight B equals fraction numerator 3 up diagonal strike straight x squared space end strike left parenthesis straight x space plus space 1 right parenthesis over denominator 2 up diagonal strike straight x squared space end strike left parenthesis straight x space plus space 2 right parenthesis end fraction space equals space fraction numerator 3 space left parenthesis straight x space plus space 1 right parenthesis over denominator 2 space left parenthesis straight x space plus space 2 right parenthesis end fraction space equals space fraction numerator 3 x plus 3 over denominator 2 x plus 1 end fraction$

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