<span>Here, we only need the upper hemisphere:
z = √(36 - x^2 - y^2).
Note that the cone and sphere intersect at z^2 + z^2 = 36 ==> z = √18
==> The region of integration is x^2 + y^2 + 18 = 36 ==> x^2 + y^2 = 18.
So via Cartesian Coordinates, the surface area equals
∫∫ √[1 + (z_x)^2 + (z_y)^2] dA
= ∫∫ √[1 + (-x/√(36 - x^2 - y^2))^2 + (-y/√(36 - x^2 - y^2))^2] dA
= ∫∫ √[1 + (x^2 + y^2)/(36 - x^2 - y^2)] dA
= ∫∫ √[36/(36 - x^2 - y^2)] dA
= ∫∫ 6 dA/√(36 - x^2 - y^2).
Converting to polar coordinates yields
∫(θ = 0 to 2π) ∫(r = 0 to √18) 6r dr dθ/√(36 - r^2)
= 2π ∫(r = 0 to √18) 6r(36 - r^2)^(-1/2) dr
= 2π * -3 * 2√(36 - r^2) {for r = 0 to √18}
= 12π (6 - 3√2)
= 36π (2 - √2).
I hope this helps! </span>
Answer:
this is outta my league
Step-by-step explanation:
Answer:
192 
Step-by-step explanation:
Given that
Volume of spherical sculpture = 256 ft³
is used as 3.
To find:
Surface area of sculpture = ?
Solution:
First of all, let us learn about the formula for Volume and Surface Area of Sphere:
1. 
2. 
Given volume is 256 ft³.
Now, let us put r = 4 in the formula of Surface Area to find the value of Surface Area:
So, approximate surface area of sculpture is 192 .
C is the answer, hope this helps!
Answer:
2500000000
Step-by-step explanation:
→ Multiply 1 by 25000
1 × 25000 = 25000
→ Convert into metres
2500000
→ Convert into centimetres
2500000000
