A 6 inch length cylindrical through hole is drilled through the center of sphere, what will be the remaining volume of sphere ?

In this question only one data is given ie., hole length -
6". In the question there is no mistake.
Find the answer.

Answers were Sorted based on User's Feedback

A 6 inch length cylindrical through hole is drilled through the center of sphere, what will be the r..

Answer / priya

But still no calculus is needed, well, not really...

Now, suppose you set out to answer the question in the absence of such specific direction as to how the answer should be given. We're going to set this sphere down on an x-axis centered right down the middle of the cylindrical hole.

let x=0 be the center of the sphere,
let r be the radius of the sphere, and
let h be the radius of the cylindrical hole.

The relationship between h and r, which we'll need later, is h² + 3² = r²

Now consider this slice of the holey sphere: Plane P is perpendicular to the axis of the hole at a directed distance of "x" from the center of the sphere, -3 ≤ x ≤ 3. The slice is the intersection of plane P with the sphere and its interior, minus the cylindrical hole: an annulus, the area bounded by a pair of concentric circles.

The radius of the smaller circle is h, and the radius of the larger circle is sqrt(r²-x²)

So the area of this slice is π(r²-x²)-π(h²) = π(r²-x² -h²)

Since r²=h²+3², (remember?), the area of this slice is π(h²+3²-x²-h²) = π(3²-x²)

This is the same as the area of a slice through a sphere of radius 3 with no hole, or with a hole whose radius is zero.

Since the cross-section area at distance x from the center of the holey sphere is the same as the cross-section area at the same distance from the center of an ordinary sphere of radius 3, it follows that the volume of the holey sphere, which is the integral of all these cross-section areas, is the same as the volume of the ordinary sphere.

The answer is (4/3)π(3³) = 36π

 Is This Answer Correct ? 0 Yes 0 No

A 6 inch length cylindrical through hole is drilled through the center of sphere, what will be the r..

Answer / shyam

volume of a sphere is 4/3 * pi * r^3
by drilling a hole 6 inches long the volume of the sphere is
not affected bcos the hole is a 1 dimension quantity..(say a
straight line) n so it does not have any value w.r.t volume...

hence the volume of the sphere does not change..

 Is This Answer Correct ? 2 Yes 3 No

A 6 inch length cylindrical through hole is drilled through the center of sphere, what will be the r..

Answer / udit

volume of sphere will not be affected, because drilling is
done through the hole of sphere.

 Is This Answer Correct ? 1 Yes 3 No

More General Aptitude Interview Questions

if 4 circles of equal radius are drawn with vertices of a square as the centre , the side of the square being 7 cm, find the area of the circles outside the square?

Some statements are given below: � L says all of my other four friends have money � M says that P said that exactly one among them has money � N says that L said that precisely two among them have money � O says that M said that three of the others have money � P, L and N said that they have money All the above statement are false.. Who has money & who doesn't have any money?

area of triangle=1/2*b*h base incresed by 4 times & height is devided by 2, the net effect of area.

Area if square increase by 69% find sides % increased by?

Raja is twice older than raghav . If Raja was 4 years younger, raghav was 3 years older ther diff. between their ages is 12 years what is the sum of thier ages

Hi i am going to prepare for RRB exam so can you please send me some Questions paper my id is salvepramods@gmail.com

can you send me the SBI Clerical post model question papers

. In june a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?

Two planes take off at the same exact moment. They are flying across the Atlantic Ocean. One leaves New York and is flying to Paris at 800 km/hr. The other leaves Paris and is flying to New York at only 750 km/hr ( because of a strong head wind ). Which one will be closer to Paris when they meet?

In an examination, 35% of the students passed and 455 failed. How many students appeared for the examination?

kaalu ki maa ke teen bache, athani, chavanni aur teesra __________????????????

There are 2 toy cars facing each other at a distance of 500 cm from each other . Each other moves forward by 100 cm at a speed of 50 cm/sec and then moves back by 50 cm at a speed of 25 cm/sec . how long will it take the cars to collide each other ?

Categories
• English (498)
• General Aptitude (2072)
• Puzzles (480)