The edges of three of the four cubes are 1, c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the edge of the fourth cube be $x\, cm$.The volume of a cube with edge $a$ is given by $V = a^3$.The volumes of the given cubes are $1^3 = 1\,

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(B) Let the edge of the fourth cube be $x\, cm$.The volume of a cube with edge $a$ is given by $V = a^3$.The volumes of the given cubes are $1^3 = 1\, cm^3$,$9^3 = 729\, cm^3$,and $10^3 = 1000\, cm^3$.According to the problem,the sum of the volumes of the cubes with edges $9\, cm$ and $10\, cm$ is equal to the sum of the volumes of the cubes with edges $1\, cm$ and $x\, cm$.So,$9^3 + 10^3 = 1^3 + x^3$.$729 + 1000 = 1 + x^3$.$1729 = 1 + x^3$.$x^3 = 1728$.Taking the cube root on both sides,$x = \sqrt[3]{1728} = 12\, cm$.Thus,the edge of the fourth cube is $12\, cm$.

The edges of three of the four cubes are $1\, cm, 9\, cm$ and $10\, cm$ respectively. If the total volume of two cubes with $9\, cm$ edge and $10\, cm$ edge is equal to the volume of the remaining two cubes,find the edge of the fourth cube in $cm$.

Similar Questions

$A$ hemispherical metallic bowl is made of steel,$0.2 \, cm$ thick. The inner radius of the bowl is $4 \, cm$. Find the outer curved surface area of the bowl (in $cm^2$).

The dimensions of a cuboidal box are in the ratio $6: 4: 3$. The difference between the cost of covering it with white paper at the rate of $₹ 2.00$ per $m^2$ and with coloured paper at the rate of $₹ 2.50$ per $m^2$ is $₹ 1350$. Find the dimensions of the box.

$1 \, m^{2} = \ldots \ldots \, cm^{2}$

The radius of the base of a cone is $7 \, cm$ and its height is $30 \, cm$. Find the volume of a cone (in $cm^3$).

The length of the longest pole that can be placed in a room of dimensions $(10 \text{ m} \times 10 \text{ m} \times 5 \text{ m})$ is (in $\text{m}$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module