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
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|
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|
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|
A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles?
a student is ranked 13th from right and 8th from left.how many are there?
0.23 + 0.02323 + 0.002323.... == ???
If a person walks at 4/5th of his usual spee he reaches 40min late. If he walks athis usual speed how much time does he travels.
A solid cube of 4 inches has been painted red, green and black on the pairs of opposite faces. It has then been cut into one inch cubes. Following questions relate to the smaller one inch cubes. 1.How many cubes have only one face painted? (1) 8 (2) 16 (3) 24 (4) 32 2. How many cubes have only two faces painted? (1) 0 (2) 16 (3) 24 (4) 32 3. How many cubes have only four faces painted? (1) 0 (2) 8 (3) 12 (4) 16 4. How many cubes have no faces painted? (1) 0 (2) 8 (3) 16 (4) 24 How to solve this
A secret can be told only 2 persons in 5 minutes .the same person tells to 2 more persons and so on . How long will take to tell it to 768 persons ?
How many bridges over yamuna river in Delhi?
What is capital expenditure and revenu expenditure
in which state does bay of bengal exist
I HAVE APPEARED FOR ALLAHABAD BANK ON 21-02-10, I WANT TO KNOW THE SECTIONAL CUT OFF'S FOR CATEGORY.
7. A new medicine has been developed and its effectiveness has been determined by carrying out an experimental study. 30 patients were divided into groups of 20 and 10. The group having 20, were given medicine while the other group dint get any medication. The results obtained where as follows:- Medication Non-medication Improved 8 2 Unimproved 12 8 Based on data, I think medication was:-