Answer:
790π
Step-by-step explanation:
We are given;
Diameter of cylinder;d = 10 mm
So, radius;r = 10/2 = 5 mm
Height of cylinder;h = 70mm
Surface area of cylinder is given by the formula; S.A = 2πr² + 2πrh
Plugging in the relevant values, we have;S.A = 2π(5)² + 2π(5)(70)
S.A = 50π + 700π
S.A = 750π
Now, because one base of the cylinder is hidden as the cone is stacked on that face, we will deduct the area of that base face;
Thus, Surface area = 750π - π(5)² = 750π - 25π = 725π
For the cone,
Height;h = 12mm
Since this is stacked directly on the cylinder, it will have the same radius. Thus; radius;r = 5mm
Now,formula for surface area of cone is;
S.A = πr² + πrL
Where L is slant height.
We can use pythagoras theorem to get L.
So, L² = r² + h²
L = √r² + h²
L = √(5² + 12²)
L = √(25 + 144)
L = √169
L = 13
So, S.A of cone = π(5)² + (π×5×13)
S.A = 25π + 65π = 90π
Similar to what was done to the Cylinder, since the circular base of the cone is stacked on the cylinder, we will deduct the surface area of that base as it is hidden.
So, S.A is now = 90π - π(5)²
= 90π - 25π = 65π
Thus,total surface area of the pencil = 725π + 65π = 790π
