A solid is in the form of a right circular cone mounted on a hemispher...
Given:
Radius of hemisphere (r1) = 2.1 cm
Height of cone (h) = 4 cm
Radius of cylinder (r2) = 5 cm
Height of cylinder (H) = 9.8 cm
To find:
Volume of water left in the tub
Solution:
Step 1: Calculate the volume of the solid
The solid is formed by a cone mounted on a hemisphere. We need to find the combined volume of the cone and hemisphere.
Volume of Hemisphere:
The volume of a hemisphere is given by the formula:
V1 = (2/3) * π * r1^3
Substituting the given value of r1 = 2.1 cm, we have:
V1 = (2/3) * 3.14 * (2.1)^3
V1 = 19.4488 cm^3 (approx.)
Volume of Cone:
The volume of a cone is given by the formula:
V2 = (1/3) * π * r2^2 * h
Substituting the given values of r2 = 5 cm and h = 4 cm, we have:
V2 = (1/3) * 3.14 * (5)^2 * 4
V2 = 104.6667 cm^3 (approx.)
Total Volume of Solid:
The total volume of the solid is the sum of the volume of the hemisphere and the volume of the cone.
V_total = V1 + V2
V_total = 19.4488 + 104.6667
V_total = 124.1155 cm^3 (approx.)
Step 2: Calculate the volume of the cylinder
The volume of a cylinder is given by the formula:
V_cylinder = π * r2^2 * H
Substituting the given values of r2 = 5 cm and H = 9.8 cm, we have:
V_cylinder = 3.14 * (5)^2 * 9.8
V_cylinder = 765.4 cm^3 (approx.)
Step 3: Calculate the volume of water left in the tub
The volume of water left in the tub is equal to the volume of the cylinder minus the total volume of the solid.
V_water_left = V_cylinder - V_total
V_water_left = 765.4 - 124.1155
V_water_left = 641.2845 cm^3 (approx.)
Therefore, the volume of water left in the tub is approximately 641.2845 cm^3, which is option A.