A cube of side 4 , cm contains a sphere touch | vedclass

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

Question

(B) Side of the cube $a = 4 \, cm$.Volume of the cube $V_{cube} = a^3 = (4)^3 = 64 \, cm^3$.Since the sphere touches the sides of the cube,the diamete

Vedclass · Accepted Answer

$30.48$

Vedclass · Answer

(B) Side of the cube $a = 4 \, cm$.Volume of the cube $V_{cube} = a^3 = (4)^3 = 64 \, cm^3$.Since the sphere touches the sides of the cube,the diameter of the sphere is equal to the side of the cube,$d = 4 \, cm$.Radius of the sphere $r = d / 2 = 4 / 2 = 2 \, cm$.Volume of the sphere $V_{sphere} = \frac{4}{3} \pi r^3 = \frac{4}{3} 	imes \frac{22}{7} 	imes (2)^3$.$V_{sphere} = \frac{4}{3} 	imes \frac{22}{7} 	imes 8 = \frac{704}{21} \approx 33.52 \, cm^3$.Volume of the gap = $V_{cube} - V_{sphere} = 64 - 33.52 = 30.48 \, cm^3$.

$A$ cube of side $4 \, cm$ contains a sphere touching its sides. Find the volume of the gap in between. (in $, cm^3$)

Similar Questions

There are two boxes of metal sheet. The length,width,and height of a cuboidal box are $30 \, cm$,$25 \, cm$,and $20 \, cm$ respectively. $A$ cubical box has each edge of $25 \, cm$. Find out which box requires more metal sheet and by how many $cm^2$?

Two solid spheres made of the same metal have weights $5920 \, g$ and $740 \, g$ respectively. Determine the radius of the larger sphere,if the diameter of the smaller one is $5 \, cm$. (in $cm$)

Write True or False and justify your answer.
$A$ right circular cylinder just encloses a sphere of radius $r$ as shown in the figure. The surface area of the sphere is equal to the curved surface area of the cylinder.

Find the surface area of a sphere of radius $50\, cm$ $(\pi = 3.14)$ (in $cm^2$).

The radius of a sphere is $6\, cm$. It is melted and drawn into a wire of diameter $1\, cm$. Find the length of the wire (in $m$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module