A toy is in the shape of a right circular cylinder with hemisphere on one end and a cone on the other . The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radius of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy if the height of the conical point is 12 cm
hemisphere: a = 2pi r^2
cone: a = pi r s
cylinder: a = pi r^2 h
total area:
2 pi * 5^2 + pi * 5 * 13 + pi * 5^2 * 13 = 440pi
where is the height of conical point = 12cm used..
only used in determining the slant height (s) of the cone. 5^2+12^2 = 13^2
To calculate the surface area of the toy, we need to determine the surface areas of each individual component (cylinder, hemisphere, and cone) and then add them together.
Let's start with the cylinder:
- The surface area of a cylinder is given by the formula 2πrh, where r is the radius and h is the height.
Given that the radius of the cylindrical part is 5 cm and the height is 13 cm, we can calculate the surface area of the cylindrical part:
Surface area of cylindrical part = 2π(5 cm)(13 cm)
Next, let's move on to the hemisphere:
- The surface area of a hemisphere is given by the formula 2πr^2, where r is the radius.
Since the radius of the hemisphere is the same as the cylindrical part (5 cm), we can calculate the surface area of the hemisphere:
Surface area of hemisphere = 2π(5 cm)^2
Finally, let's calculate the surface area of the cone:
- The surface area of a cone is given by the formula πr(r + √(r^2 + h^2)), where r is the radius and h is the slant height (the height of the conical point).
Given that the radius of the cone is the same as the cylindrical part (5 cm) and the height of the conical point is 12 cm, we can calculate the surface area of the cone:
Surface area of cone = π(5 cm)[5 cm + √(5 cm)^2 + (12 cm)^2]
Now, we can add up the surface areas of the three components to get the total surface area of the toy:
Total surface area = Surface area of cylindrical part + Surface area of hemisphere + Surface area of cone
Lastly, we substitute the calculated values into the formulas and perform the necessary calculations to find the final answer.