A city park contains a cylindrical artificial pond that has a radius of 7.5m. A 2m concrete deck will be constructed around the pond. The concrete should be at least 15 cm thick. Calculate the...

A city park contains a cylindrical artificial pond that has a radius of 7.5m.

A 2m concrete deck will be constructed around the pond. The concrete should be at least 15 cm thick.

Calculate the minimum volume of concrete required to construct the deck, to one decimal place?

Asked on by knemat1988

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

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 `

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You will need approximately 16.02 cubic meters of concrete.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

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