a dog toy is constructed in the shape of a cylinder with a length of 6.8 in. The cylinder has a hemisphere at each end. The diameter is 1-9 in. Find the volume.
1-9 is not a diameter. You probably made a typing error.
The volume will be pi[R^2*L + (4R^3)/3]
Get the radius R from the diameter.
To find the volume of the dog toy, we need to calculate the volumes of the cylindrical part and the two hemispherical parts separately, and then add them up.
First, let's find the volume of the cylinder.
The formula for the volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height.
Since we know the length of the cylinder is 6.8 inches, and the diameter is given as 1-9 inches, we can calculate the radius by dividing the diameter by 2.
The radius (r) of the cylinder is (1-9)/2 = 0.5 inches.
Now, we can calculate the volume of the cylinder using the formula: V_cylinder = π(0.5^2)(6.8).
V_cylinder = 3.14 * 0.25 * 6.8.
V_cylinder ≈ 5.37 cubic inches.
Next, let's find the volume of the two hemispheres.
The formula for the volume of a hemisphere is given by V = (2/3)πr^3.
Since the diameter of the cylinder is given as 1-9 inches, the radius (r) of the hemisphere is (1-9)/2 = 0.5 inches.
Now, we can calculate the volume of one hemisphere using the formula: V_hemisphere = (2/3) * 3.14 * (0.5^3).
V_hemisphere ≈ 0.52 cubic inches (for one hemisphere).
Since there are two hemispheres in the dog toy, the total volume of the hemispheres is 2 * 0.52 = 1.04 cubic inches.
Finally, to find the total volume of the dog toy, we add the volume of the cylinder and the volume of the hemispheres:
Total volume = V_cylinder + V_hemispheres.
Total volume ≈ 5.37 + 1.04.
Total volume ≈ 6.41 cubic inches.
Therefore, the volume of the dog toy is approximately 6.41 cubic inches.