7.
a. a 3×5 rectangle is revolved about one of its sides of length 5 to create a solid of revolution. find volume of the solid.
b. a 3-4-5 right triangle is revolved about a leg of length 4 to create a solid of revolution. describe the solid.
c. a 3-4-5 right triangle is revolved about its legs to create two solids. find the volume of each solid

a. 45 π

b. 12 π

c. 16 π

Step-by-step explanation:

a.

If a 3×5 rectangle is revolved about one of its sides of length 5 to create a solid of revolution, we can see a cilinder with:

Radius: 3

Height: 5

Then the volume of the cylinder is:

V=π*r^{2} *h= π*(3)^{2} *(5) = π*(9)*(5)=45 π

b. If a 3-4-5 right triangle is revolved about a leg of length 4 to create a solid of revolution. We can see a cone with:

Radius: 3

Height: 4

Then the volume of the cone is:

V=(1/3)*π*r^{2} *h= (1/3)*π*(3)^{2} *(4) = (1/3)*π*(9)*(4)=12 π

c. We can answer this item using the past (b. item) and solving for the other leg revolution (3):

Then we will have:

Radius: 4

Height: 3

Then the volume of the cone is:

V=(1/3)*π*r^{2} *h= (1/3)*π*(4)^{2} *(3) = (1/3)*π*(16)*(3)=16 π

-1, -2, -3, -4, -6

step-by-step explanation: