Question

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

a) 165.5 cm²
b) 175.0 cm²
c) 185.5 cm²
d) 195.0 cm²

Answer 1

To find the total surface area of the toy, calculate the surface areas of the cone and the hemisphere, and then add them together. The total surface area is approximately 185.5 cm².

Step-by-step explanation:

To find the total surface area of the toy, we need to calculate the individual surface areas of the cone and the hemisphere, and then add them together.

Surface area of the cone = πr(l + r), where r is the radius of the base and l is the slant height.
In this case, r = 3.5 cm and l = h = 15.5 cm (since the total height is the same as the slant height).

Surface area of the hemisphere = 2πr², where r is the radius.
In this case, r = 3.5 cm.

Adding the two surface areas together, we get:
Total surface area = Surface area of cone + Surface area of hemisphere = π(3.5)(15.5 + 3.5) + 2π(3.5)².

Calculating this expression, we find that the total surface area of the toy is approximately 185.5 cm².