Turito Academy

Test Prep

Global form fields

Explanations: Step 1 of 1: Let the length of the edge of the metal cube be a. Volume of cube = a3 Given,  r = 30/2 cm and h = <img src="data:image/png;base64,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" class="Wirisformula" alt="1 41 over 99 cm" width="61" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«mfrac»«mn»41«/mn»«mn»99«/mn»«/mfrac»«mi»cm«/mi»«/math»'/> By the principle of Archimedes, Volume of risen milk = volume of cube <img src="data:image/png;base64,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" class="Wirisformula" alt="not stretchy rightwards double arrow pi open parentheses 30 over 2 close parentheses squared cross times 1 41 over 99 equals a cubed" width="173" height="41" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo stretchy=¨false¨»§#8658;«/mo»«mi»§#960;«/mi»«msup»«mfenced separators=¨|¨»«mfrac»«mn»30«/mn»«mn»2«/mn»«/mfrac»«/mfenced»«mn»2«/mn»«/msup»«mo»§#215;«/mo»«mn»1«/mn»«mfrac»«mn»41«/mn»«mn»99«/mn»«/mfrac»«mo»=«/mo»«msup»«mi»a«/mi»«mn»3«/mn»«/msup»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="not stretchy rightwards double arrow a cubed equals 1000" width="95" height="16" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo stretchy=¨false¨»§#8658;«/mo»«msup»«mi»a«/mi»«mn»3«/mn»«/msup»«mo»=«/mo»«mn»1000«/mn»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="not stretchy rightwards double arrow a equals 10" width="67" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo stretchy=¨false¨»§#8658;«/mo»«mi»a«/mi»«mo»=«/mo»«mn»10«/mn»«/math»'/>, discarding the negative value since distance cannot be negative. Final Answer: The length of the edge of the cube is 10cm.

When a solid metal cube is completely submerged in a cylindrical vessel Containing milk with 30 cm diameter the level of milk rises by <img src="data:image/png;base64,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" class="Wirisformula" alt="1 41 over 99" width="38" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«mfrac»«mn»41«/mn»«mn»99«/mn»«/mfrac»«/math»'/> cm. Find the length of the edge of the metal cube.

Solution for the question - when a solid metal cube is completely submerged in a cylindrical vesselcontaining milk with 30 cm diameter the level of milk rises b