The estimated total surface area of the cake baked in the circular cake pan is approximately 285.89 cm².
The area of a circular cake can be determined using the formula for the area of a circle, which is A = πr², where A is the area and r is the radius. In this case, the radius of the cake pan is 7 cm. Plugging this value into the formula, we get:
A = π * (7 cm)²
Calculating this gives us the area of the circular cake as approximately 153.94 cm².
To account for the depth of the cake pan, we also need to consider the lateral surface area of the cylindrical shape. The formula for the lateral surface area of a cylinder is A_cylinder = 2πrh, where r is the radius and h is the height (depth) of the cylinder. For the cake pan, with a radius of 7 cm and a depth of 3 cm:
A_cylinder = 2π * 7 cm * 3 cm
Calculating this gives us the lateral surface area of the cake pan as approximately 131.95 cm².
To find the total surface area of the cake, we add the area of the circular top and bottom to the lateral surface area:
A_total = A + A_cylinder
A_total = 153.94 cm² + 131.95 cm²
A_total is approximately 285.89 cm².
The question probable may be:
Estimate the area of a cake baked in a circular cake pan whose radius is 7 cm and the pan is 3cm deep.