(A) Let the side length of the cube be $l$.Given that the volume $V$ is equal to the surface area $A$:$V = A$$l^3 = 6l^2$Dividing both sides by $l^2$

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(A) Let the side length of the cube be $l$.Given that the volume $V$ is equal to the surface area $A$:$V = A$$l^3 = 6l^2$Dividing both sides by $l^2$ (since $l \neq 0$):$l = 6$Now,the volume $V$ is:$V = l^3 = (6)^3 = 216 \text{ cubic units}$.

Class 11 Physics Units, Dimensions and Measurement Mix Examples-Units, Dimensions and Measurement

Medium

If the volume and surface area of a cube are numerically equal,what is its volume in cubic units?

A
$216$
B
$36$
C
$6$
D
$1296$

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Class 11

Physics Questions

Chapter

Units, Dimensions and Measurement

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Mix Examples-Units, Dimensions and Measurement

Match List $I$ with List $II$:

List $I$ List $II$

$A$. Torque $I$. $[M^1 L^1 T^{-2} A^{-2}]$

$B$. Magnetic field $II$. $[L^2 A^1]$

$C$. Magnetic moment $III$. $[M^1 T^{-2} A^{-1}]$

$D$. Permeability of free space $IV$. $[M^1 L^2 T^{-2}]$

Choose the correct answer from the options given below:

DifficultJEE MAIN 2024

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Pressure exerted by a gas is found to be $50\, N/m^2$. What is the value of this pressure in the $CGS$ system?

Easy

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Match List $I$ with List $II$ and select the correct answer using the codes given below the lists:

List $I$ List $II$

$P.$ Boltzmann constant $1.$ $[ML^2T^{-1}]$

$Q.$ Coefficient of viscosity $2.$ $[ML^{-1}T^{-1}]$

$R.$ Planck constant $3.$ $[MLT^{-3}K^{-1}]$

$S.$ Thermal conductivity $4.$ $[ML^2T^{-2}K^{-1}]$

Codes: $P \quad Q \quad R \quad S$

DifficultIIT 2013

View Solution

Write the unit and dimensional formula of the ratio of the gravitational constant $(G)$ to the acceleration due to gravity $(g)$.

Medium

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Which of the following pairs does not have the same dimensions?

Easy

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List $I$	List $II$
$A$. Torque	$I$. $[M^1 L^1 T^{-2} A^{-2}]$
$B$. Magnetic field	$II$. $[L^2 A^1]$
$C$. Magnetic moment	$III$. $[M^1 T^{-2} A^{-1}]$
$D$. Permeability of free space	$IV$. $[M^1 L^2 T^{-2}]$

List $I$	List $II$
$P.$ Boltzmann constant	$1.$ $[ML^2T^{-1}]$
$Q.$ Coefficient of viscosity	$2.$ $[ML^{-1}T^{-1}]$
$R.$ Planck constant	$3.$ $[MLT^{-3}K^{-1}]$
$S.$ Thermal conductivity	$4.$ $[ML^2T^{-2}K^{-1}]$

If the volume and surface area of a cube are numerically equal,what is its volume in cubic units?

Similar Questions

Match List $I$ with List $II$: List $I$ List $II$ $A$. Torque $I$. $[M^1 L^1 T^{-2} A^{-2}]$ $B$. Magnetic field $II$. $[L^2 A^1]$ $C$. Magnetic moment $III$. $[M^1 T^{-2} A^{-1}]$ $D$. Permeability of free space $IV$. $[M^1 L^2 T^{-2}]$ Choose the correct answer from the options given below:

Pressure exerted by a gas is found to be $50\, N/m^2$. What is the value of this pressure in the $CGS$ system?

Write the unit and dimensional formula of the ratio of the gravitational constant $(G)$ to the acceleration due to gravity $(g)$.

Which of the following pairs does not have the same dimensions?

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Match List $I$ with List $II$:

List $I$ List $II$

$A$. Torque $I$. $[M^1 L^1 T^{-2} A^{-2}]$

$B$. Magnetic field $II$. $[L^2 A^1]$

$C$. Magnetic moment $III$. $[M^1 T^{-2} A^{-1}]$

$D$. Permeability of free space $IV$. $[M^1 L^2 T^{-2}]$

Choose the correct answer from the options given below: