Answer :
To solve this problem, we need to find the volume of the original cuboid and then use it to calculate the height of the resulting cylindrical solid.
Given information:
- Dimensions of the cuboid: 11 cm × 14 cm × 5 cm
- Diameter of the cylindrical solid: 28 cm
Step 1: Calculate the volume of the cuboid.
Volume of the cuboid = Length × Width × Height
Volume of the cuboid = 11 cm × 14 cm × 5 cm = 770 cm³
Step 2: Calculate the volume of the cylindrical solid.
Volume of a cylinder = π × r² × h
Where:
- r is the radius of the cylinder (half the diameter)
- h is the height of the cylinder
Substituting the given values:
Volume of the cylinder = π × (28 cm / 2)² × h
Volume of the cylinder = π × 14² × h
Volume of the cylinder = 616 π cm³
Step 3: Set the volume of the cuboid equal to the volume of the cylinder and solve for the height of the cylinder.
Volume of the cuboid = Volume of the cylinder
770 cm³ = 616 π cm³
h = 770 cm³ / (616 π cm³)
h = 1.25 cm
Therefore, the height of the cylindrical solid is approximately 1.25 cm.
Given information:
- Dimensions of the cuboid: 11 cm × 14 cm × 5 cm
- Diameter of the cylindrical solid: 28 cm
Step 1: Calculate the volume of the cuboid.
Volume of the cuboid = Length × Width × Height
Volume of the cuboid = 11 cm × 14 cm × 5 cm = 770 cm³
Step 2: Calculate the volume of the cylindrical solid.
Volume of a cylinder = π × r² × h
Where:
- r is the radius of the cylinder (half the diameter)
- h is the height of the cylinder
Substituting the given values:
Volume of the cylinder = π × (28 cm / 2)² × h
Volume of the cylinder = π × 14² × h
Volume of the cylinder = 616 π cm³
Step 3: Set the volume of the cuboid equal to the volume of the cylinder and solve for the height of the cylinder.
Volume of the cuboid = Volume of the cylinder
770 cm³ = 616 π cm³
h = 770 cm³ / (616 π cm³)
h = 1.25 cm
Therefore, the height of the cylindrical solid is approximately 1.25 cm.
