From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.Solution:

To find the total surface area of the remaining solid, we need to calculate the surface area of the cylinder and subtract the surface area of the conical cavity.

Step 1: Calculate the surface area of the cylinder. The formula for the surface area of a cylinder is given by: Surface Area of Cylinder = 2πr(r + h) where r is the radius and h is the height of the cylinder.

Given that the diameter of the cylinder is 1.4 cm, we can calculate the radius as follows: Radius = diameter/2 = 1.4 cm/2 = 0.7 cm

Substituting the values into the formula, we get: Surface Area of Cylinder = 2π(0.7 cm)(0.7 cm + 2.4 cm)

Step 2: Calculate the surface area of the conical cavity. The formula for the surface area of a cone is given by: Surface Area of Cone = πr(r + √(r^2 + h^2)) where r is the radius and h is the height of the cone.

Since the conical cavity has the same height and diameter as the cylinder, the radius of the conical cavity is also 0.7 cm.

Substituting the values into the formula, we get: Surface Area of Cone = π(0.7 cm)(0.7 cm + √(0.7 cm^2 + 2.4 cm^2))

Step 3: Calculate the total surface area of the remaining solid. To find the total surface area, we subtract the surface area of the conical cavity from the surface area of the cylinder: Total Surface Area = Surface Area of Cylinder - Surface Area of Cone

Finally, we can substitute the calculated values into the equation and find the total surface area of the remaining solid.