Question

¿How you solve?

A pool is 8 m long, 6 m wide and 1.5 m deep. It is painted at $6 per square meter.

a) How much will it cost to paint it?
b) How many litres of water will be needed to fill it?

Answer 1

9514 1404 393

Answer:

a) $540 cost to paint

b) 72000 liters to fill

Explanation:

Relevant formulas are ...

P = 2(L +W) . . . . perimeter of a rectangle of length L and width W

A = LW . . . . . . area of a rectangle of length L and width W

V = LWH . . . volume of a cuboid of length L, width W, and height H

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a) The total painted area is the area of the pool walls plus the area of the pool bottom. The wall area is the product of pool perimeter and wall height. The bottom area is the product of pool length and width.

A = PH + LW = 2(L +W)H +LW

A = 2(8 m +6 m)(1.5 m) + (8 m)(6 m) = 42 m² +48 m² = 90 m²

At $6 per square meter, the cost of painting the pool is ...

($6 /m²)(90 m²) = $540 . . . . cost to paint the pool

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b) The volume in liters is best figured using the dimensions in decimeters.

V = (80 dm)(60 dm)(15 dm) = 72000 dm³ = 72000 L

72000 liters will be needed to fill the pool.