Answer Posted / 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

All birds are animals. All animals are four legged. Implications a. All animals which are four legged are birds. b. All birds are four legged c. Some birds are four legged d. Some birds are animals but not four legged.

1827

---

x + 4 y relation between x and y is x/2y = 3/2 ie x = 3y find the x -2y ratio

1069

---

p and q are positive integers with their average 5, find how many different values can p take

1211

---

Find the correct meaning of the following phrase: To be in the air

1172

---

what is the syllabus for group-1 and upsc exam for ias also specify the age limit for both appsc and upsc exams. is there any age relaxation for divorced women.

3495

---

Alphametics are puzzles where each letter stands for a different digit. Here are two alphametics. No word can begin with a zero. We’ve started you out with some of the letters. BASE + BALL -------------- GAMES what these alphabets represent

4821

---

In a 10 digit number, if the 1st digit number is the number of ones,2nd digit number is the number of twos, and ... so on. 10th digit is the number of zeroes,then find the number

1179

---

distance D=rt where r & t are +ve and r is constant,as t increases then D_________

1242

---

There are A,B techers and C,D doctors.Find the possible no of combinations that should not be repeated more than once?

1294

---

Zulus always speak truth and Hutus always speak lies. There are three persons A,B&C. A met B and says " I am a Zulu or I am Hutu". We don't know what exactly he said. then B meets C and says to c that " A is a Zulu ". Then C replied " No, A is a Hutu ". How many Zulus are there ?

1495

---

In a group of 15 students,7 of them have studied Marathi, 8 of them have studied History, and 3 have not studied either. How many students studied both Marathi and History?

1129

---

2 Oranges,3 bananas and 4 apples cost rs.15 . 3 Oranges 2 bananas 1 apple costs rs 10. What is the cost of 3 oranges, 3 bananas and 3 apples

1223

---

What is the error in the given sequence. 2,3 6,7 14,15 29,46.

1134

---

Every day a driver comes to pick up a man at his office at 6pm. One day the man gets free early and rather than waiting for the driver, he starts walking for home at 4:30pm. The man meets the driver on the way and then reaches home 30minutes earlier than usual. What is the usual time that man takes to reach home from the office?

1228

---

What is the max possible 3 digit prime number?

1188

---