Question

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 15cm thick. Calculate the minimum volume of concrete required to construct the deck, to one decimal place. Please Draw a diagram.

Answer 1

Given:

a.) City park contains a cylindrical artificial pond that has a radius of 7.5m.

b.) A 2m concrete deck will be constructed around the pond.

c.) The concrete should be at least 15cm thick.

Let's draw the scenario to better understand the problem:

Step 1: Area of the Pond.

$\text{ Area}_{POND}\text{ = \pi r}^2\text{ = \lparen3.1416\rparen\lparen7.5\rparen}^2\text{ = \lparen3.1416\rparen\lparen56.25\rparen}$$\text{ Area}_{POND}\text{ = 176.715 }\approx\text{ 176.72 m}^2$

Step 2: Area of the Pond + Deck.

$\text{ Area}_{POND\text{ + DECK}}\text{ = }\pi\text{r}^2\text{ = \lparen3.1416\rparen\lparen9.5\rparen}^2\text{ = \lparen3.1416\rparen\lparen90.25\rparen}$$\text{ Area}_{POND\text{ + DECK}}\text{ = 283.5294 }\approx\text{ 283.53 m}^3$

Step 3: Let's determine the area of the deck.

$\text{ Area}_{DECK}\text{ = Area}_{POND\text{ + DECK}}\text{ - Area}_{POND}$$\text{ = 283.53 - 176.72}$$\text{ Area}_{DECK}\text{ = 106.81 m}^2$

Step 4: Let's determine the volume of the deck.

$\text{ Volume = Area}_{DECK}\text{ x Thickness = 106.81 m}^2\text{ x 15 cm = 106.81 m}^2\text{ x 0.15 m}$$\text{ Volume = 16.0215 }\approx\text{ 16.0 m}^3$

Therefore, the minimum volume of concrete required to construct the deck is approximately 16 m³