A solid consisting of 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
Answers
Step-by-step explanation:
We need to calculate the volume of the solid figure
The figure is made of two shapes:
Conical part
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