math world problem, need answer ASAP

Question

the world cup rugby ball is shown, its is made of a cylinder with ends which are hemispheres. the ends of the cylinder and hemisphere have a radius of 8cm and the enitre ball has a length of 25cm.

 

a) calculate the surface area of the ball

 

b) find the cost to cover the ball in synthetic leather that costs $0.11/cm^2

Answer 1

Here is what i understand from the problem... 

 

We have the middle section which is a cylinder and has a radius 8 cm. 

So surface area for the cylindrical part of the ball will be only the curved surface = 2∏ r H, where H is the length of the cylinder and r the radius. 

we know r =8cm

Now the entire length of the ball is 25 cm. The two ends have hemispheres with radius 8cm. So the cylindrical part has length = 25-8-8 = 9 cm. So H = 9cm 

So surface area = 452.39 sq cm..............(1)

 

Now the two ends of the ball are hemispheres with radius 8cm. surface area of the 2 hemispheres for the ball is the curved portion of the 2 hemispheres and combined will be 4∏r²  = 804.25 sq cm.....................(2)

 

Now we add the 2 areas and get the surface area of the ball = 1256.64 sq cm

 

That is your answer for part (a)

 

 

Now for the part (b) to get the cost we multiply the surface area by the cost for unit area = 1256.64*0.11 = 138.23 $