Geumath malah 17.pdf 1/21
* 16 The diagram shows a swimming pool in the shape of a prism.
10 m
Sm
Diagram NOT
accurately drawn
וו 1
2 m
4m
DO NOT WRITE IN THIS AREA
2 m
The swimming pool is empty.
Water from 3 water tankers is going to be put into the pool.
There are 20000 litres of water in each water tanker.
Sam thinks that the surface of the water in the pool will be 10 cm below the top of the pool.
Is Sam correct?
You must show how you get your answer.
(lm - 1000 litres)
TE IN THIS AREA

9514 1404 393

  Sam is not correct.

Step-by-step explanation:

As shown in the attachment, the "base" (front face) of this prism can be divided into a rectangle and a trapezoid. The relevant area formulas are ...

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

  A = 1/2(b1 +b2)h . . . . area with parallel bases b1 and b2 and height h

__

The rectangle portion of the "base" of the pool has area ...

  A = (10 m)(1 m) = 10 m²

The trapezoid portion of the "base" of the pool has area ...

  A = 1/2(6 m +2 m)(1 m) = 4 m²

Then the "base" area is ...

  B = 10 m² +4 m² = 14 m²

__

The volume of the prism is given by ...

  V = Bh . . . . where B is the base area and h is the distance between bases

  V = (14 m²)(5 m) = 70 m³

We are told that 1 m³ = 1000 L and that 3 tankers of 20,000 L each are emptied into the pool. That leaves an unfilled volume of ...

  70 m³ -3×(20 m³) = 10 m³ . . . . unfilled volume

__

The surface area of the pool is ...

  A = LW = (10 m)(5 m) = 50 m²

So the unfilled volume has a height of ...

  V = Bh

  10 m³ = (50 m²)h

  h = (10/50) m = 20/100 m = 20 cm . . . . . the height of the unfilled space

The water in the pool will be 20 cm below the top, not 10 cm. Sam is not correct.

(-5,-28)

i graphed to on desmos.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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