A deck 2m wide is to be built around a cylindrical pond of radius 7.5m; the concrete is to be at least 15cm thick:

The formula for the volume of an annulus is `V=pi(R^2-r^2)h ` where R is the outer radius and r is the inner radius. Here we have R=9.5m, r=7.5m, and h=.15m (Note the conversion to a common measurement; in this case meters.)

((Another way to see this is to calculate the volume of a cylinder that encompasses the pond and the deck and then subtract away the volume for the pond. `V_p=pi(7.5)^2h,V_t=pi(9.5)^2h ` so `V_d=V_t-V-p=pih(9.5^2-7.5^2) ` ))

Then `V=pi(9.5^2-7.5^2)(.15)=pi(34)(.15)=5.1pi~~16.02212253 `

------------------------------------------------------------------------------------------------

You will need approximately 16.02 cubic meters of concrete.

-------------------------------------------------------------------------------------------------

A cylindrical deck of height 15 cm is being built around the artificial pond with radius 7.5 m. The deck has to be 2 m wide.

The volume of the concrete required for the deck is equal to `pi*(7.5+2)^2*0.15 - pi*(7.5^2)*0.15 `

= `pi*9.5^2*0.15 - pi*7.5^2*0.15`

= 16.0 cm^3

**16 cubic meter of concrete is required to construct the
deck.**

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.