Posted by **andy** on Thursday, July 25, 2013 at 2:10pm.

Let V be the volume of the region bounded by x^2+y^2≥z^2, z≥0 and x^2+y^2+z^2≤1. What is the value of ⌊100V⌋?

- calculus -
**Steve**, Thursday, July 25, 2013 at 2:44pm
The region is inside a sphere, outside the cone. So, just find the volume of the cone with a spherical cap, and subtract that from half the sphere.

a web search will quickly provide the formulas needed.

Or, you can resort to a volume integral, most easily done using spherical coordinates.

- calculus -
**andy**, Thursday, July 25, 2013 at 3:08pm
could you give me a bit help on how to proceed if I were to use a volume integral?

- calculus -
**Steve**, Thursday, July 25, 2013 at 3:27pm
the cone is φ = π/4

the sphere is r = 1

dV = r^2 sinφ dφ dθ dr

V = ∫[0,1]∫[0,2π]∫[0,π/4] r^2 sinφ dφ dθ dr

Good luck. Probably ought to verify with cone/sphere formulas to be sure.

- calculus -
**andy**, Thursday, July 25, 2013 at 3:39pm
ok, thanks

## Answer this Question

## Related Questions

- Calculus - Evaluate ∬R xy dA, where R is the region bounded by x^2+y^2&#...
- 7th grade math help Ms. Sue - 3. Which of the following equations has an ...
- 7th grade math Ms. Sue please - 1. m 7 < 6 (1 point) m < 1 m > 1 m &...
- algebra. help! - 1. 3x+10≥4 a. x≥-2 b. x≤ 2 c. x≤-2 d. x...
- linear programming - Minimize z = 3x + 6y subject to: 4x + y ≥ 20 x + y...
- Math - Solve this linear programming problem using the simplex method: Maximize ...
- PRE-ALGEBRA MRS.SUE PLEASE!!!!!!!!! - 1. 5h 9 = 16 + 6h (1 point) 4 7 7 10 2...
- 7th grade math Ms. Sue please - 1. 5h 9 = 16 + 6h (1 point) 4 7 7 10 2. 4x...
- Mathforme - 5. 4x + 2 = x + 8. (1 point) x = 4 x = 3 x = 2 x = 1 Solve the ...
- kbMath - 5. 4x + 2 = x + 8. (1 point) x = 4 x = 3 x = 2 x = 1 Solve the ...