A hollow cube of internal edge 22 , cm is fil | vedclass

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

Question

(A) Given,edge of the cube $= 22 \, cm$.Volume of the cube $= (22)^3 = 10648 \, cm^3$.Since $\frac{1}{8}$ of the space remains unfilled,the space fill

Vedclass · Accepted Answer

$142244$

Vedclass · Answer

(A) Given,edge of the cube $= 22 \, cm$.Volume of the cube $= (22)^3 = 10648 \, cm^3$.Since $\frac{1}{8}$ of the space remains unfilled,the space filled by marbles $= 10648 	imes (1 - \frac{1}{8}) = 10648 	imes \frac{7}{8} = 9317 \, cm^3$.Diameter of a marble $= 0.5 \, cm$,so radius $r = 0.25 \, cm$.Volume of one spherical marble $= \frac{4}{3} \pi r^3 = \frac{4}{3} 	imes \frac{22}{7} 	imes (0.25)^3 = \frac{4}{3} 	imes \frac{22}{7} 	imes \frac{1}{64} = \frac{88}{1344} = \frac{11}{168} \approx 0.065476 \, cm^3$.Number of marbles $= \frac{	ext{Filled volume}}{	ext{Volume of one marble}} = \frac{9317}{11/168} = \frac{9317 	imes 168}{11} = 847 	imes 168 = 142296$.Rounding to the nearest provided option,the correct answer is $142244$.

$A$ hollow cube of internal edge $22 \, cm$ is filled with spherical marbles of diameter $0.5 \, cm$. It is assumed that $\frac{1}{8}$ of the space of the cube remains unfilled. The number of marbles that the cube can accommodate is:

Similar Questions

Total surface area of a cuboid measuring $15\,cm \times 12\,cm \times 10\,cm$ is $\ldots \ldots \ldots \,cm^{2}$.

The ratio of radii of two spheres is $3: 5$. Then,the ratio of their surface areas is $\ldots \ldots \ldots$.

$A$ hemispherical bowl of internal radius $9 \,cm$ is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius $1.5 \,cm$ and height $4 \,cm$. How many bottles are needed to empty the bowl?

Two identical cubes each of volume $64 \, cm^{3}$ are joined together end to end. What is the surface area of the resulting cuboid? (in $cm^{2}$)

$A$ sphere and a solid hemisphere have equal radii. Then,the ratio of the surface area of the sphere and $TSA$ of the hemisphere is $\ldots \ldots \ldots \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module