A pencil has a cylindrical body with a cone-shaped end. The cylinder is 5 cm long with a radius of 0.29 cm. The cone has a slant height of 1 cm and has the same radius as the cylinder. Determine the surface area of the pencil to the nearest tenth of a square centimeter.
so we are looking at
area of base of cylinder + area of sleeve of cylinder + area of cone without its base
= π(.29)^2 + 2π(.29)(5) + π(.29)(1)
= ....
you do the button pushing
(surface area of cone = πr^2 + πrs, where s is the slant height of the cone.
We only needed the πrs part)
To find the surface area of the pencil, we need to find the areas of the cylindrical body and the cone-shaped end separately, and then add them together.
Let's start with the cylindrical body:
The formula to find the surface area of a cylinder is given by:
Surface Area of Cylinder = 2πr(height + radius)
Given that the radius (r) of the cylindrical body is 0.29 cm and the height is 5 cm, we can calculate the surface area of the cylindrical body as:
Surface Area of Cylinder = 2π(0.29)(5 + 0.29) = 2π(0.29)(5.29)
Now let's move on to the cone-shaped end:
The formula to find the surface area of a cone is given by:
Surface Area of Cone = πr(slant height + radius)
Given that the slant height is 1 cm and the radius is equal to the radius of the cylindrical body (0.29 cm), we can calculate the surface area of the cone-shaped end as:
Surface Area of Cone = π(0.29)(1 + 0.29) = π(0.29)(1.29)
To find the total surface area of the pencil, we simply add the surface areas of the cylindrical body and the cone-shaped end:
Total Surface Area = Surface Area of Cylinder + Surface Area of Cone
Now, you can calculate each component and find the total surface area of the pencil to the nearest tenth of a square centimeter.