The sample space is: (1, 1); (1, 2) - sum of 3; (1, 3); (1, 4); (1, 5) - sum of 6; (1, 6); (2, 1) - sum of 3; (2, 2); (2, 3); (2, 4) - sum of 6; (2, 5); (2, 6); (3, 1); (3, 2); (3, 3) - sum of 6; (3, 4); (3, 5); (3, 6) - sum of 9; (4, 1); (4, 2) - sum of 6; (4, 3); (4, 4); (4, 5) - sum of 9; (4, 6); (5, 1) - sum of 6; (5, 2); (5, 3); (5, 4) - sum of 9; (5, 5); (5, 6); (6, 1): (6, 2); (6, 3) - sum of 9; (6, 4); (6, 5); (6, 6)
The volume of a sphere is calculated like so: v = 4*pi*r^3/3 so half sphere will have half that volume: v = (<span>4*pi*r^3/3)(1/2) </span>v = <span>4*pi*r^3/6 </span>plug in the data: v = <span>4*pi*(10)^3/6 </span>v = 2094.4 that is the volume of the half sphere