Question

a solid consisting of a right circular cone of height 120 cm and radius 60 CM standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom find the volume of water left in the cylinder if the radius of the cylinder is 60 cm and its height is 180 cm


please help to solve it guys

Answer 1

Answer:

Step-by-step explanation:

We need to calculate the volume of the solid figure

The figure is made of two shapes:

1. Conical part
2. Hemispherical part

Step 1 : Calculate the volume of the conical part:

The following is the formula of calculating the volume of a cone:

        1/3 πr²H

Volume = 1/3 × 3.142 × 60 × 60 x 120

            = 452448 cm³

Step 2: Calculate the volume of the hemispherical part

Formula for calculating the volume of a hemisphere

       2/3πr³

Volume =    2/3 × 3.142 × 60 × 60 × 60

            =    452448 cm³

∴ The volume of the solid is:

     452448 + 452448 = 904896 cm³

Volume = 904896 cm³

Step 3: Find the volume of the cylinder:

Formula of calculating the volume of a cylinder

       πr²H

Volume = 3.142 × 60 × 60 × 180

            =  2036016 cm³

⇒The volume of the water remaining in the cylinder will the volume of the solid  subtracted from the volume of the cylinder.

2036016 cm³  - 904896 cm³   = 1131120 cm³

The volume of the water left is 1131120 cm³