Answer the following question.

THERE. CHAPTER 4: TRIPLE INTEGRAL TUTORIAL 4.3 SPHERICAL COORDINATES 1. Use triple integral in spherical coordinates to find the volume of the solids a. Find the volume of the solid that lies in the first octant and is bounded by the sphere p = 2, the coordinates planes, the cone $ = - and the coned = = b. Find the volume of the solid that lies above the cone z = x2 + y2 and inside the sphere x2 + y? + zz = 4z 2. Use spherical coordinates to evaluate the integrals a. J. cos (x2 + y2 + z?)3dV where G is the solid bounded by z = 0 and z = v1 -x2 -y2 b. JUS x + y+ z dV where G is the solid bounded by z = 0 and z = \\4 -x2 -y2 3. Evaluate the integrals by changing the coordinates to spherical coordinates a. 2 4-xz Jazty (x2 +y' + z? )dz dy dx b. Izl_ v 4- x= J-/4-x2_ya dz dy dx Answer: la.= (V3 - 1)n 1b. 8x 2a. 2/3 (sin 1) 2b. 4x 28 32 5( 4/2-1)1 = 66.63 3b, 21 3