Question 7(3 points)

A pool of the shape of an inverted truncated pyramid as shown in the following figure is filled with water up to 3 meters deep.The top of the pool is a square of side-length 10 meters, the bottom of the pool is a square of side-length 2 maters, and the depth of the pool is 4 meters.The area of a horizontal layer of waterxmeters under the nozzle isA(x) = (12

{"version":"1.1","math":"$-$"}2x)²m².

See this figure.

Assume the density of water is

{"version":"1.1","math":"$\rho$"}km/m³, and let the gravity of acceleration begm/sec².The work, in Joules, needed to pump all the water in the tank to a nozzle 1 meter above the top of the tank is calculated by the integral

Question 7 options:

a)

g

4

1

x(122x)

2

dx

{"version":"1.1","math":"\( ho g\int_1^4 x(12-2x)^2dx\)"}

b)

g

4

1

(122x)

2

(1+x)dx

{"version":"1.1","math":"\( ho g\int_1^4 (12-2x)^2(1+x)dx\)"}

c)

g

5

2

(122x)

2

(5x)dx

{"version":"1.1","math":"\( ho g\int_2^5 (12-2x)^2(5-x)dx\)"}

d)

g

3

0

x(122x)

2

dx

{"version":"1.1","math":"\( ho g\int_0^3 x(12-2x)^2dx\)"}

e)

g

5

2

x(122x)

2

dx

{"version":"1.1","math":"\( ho g\int_2^5 x(12-2x)^2dx\)"}

f)

g

5

2

(122x)

2

(2+x)dx

Question 7 (3 points) A pool of the shape of an inverted truncated pyramid as shown in the following gure is lled with water up to 3 meters deep. The top of the pool is a square of side-length 10 meters, the bottom of the pool is a square of side-length 2 maters, and the depth of the pool is 4 meters. The area of a horizontal layer of water x meters under the nozzle is A(x) = (12 2x)2 m2. See this gure. Assume the density of water is p km/m3, and let the gravity of acceleration be g m/secl. The work, in Joules, needed to pump all the water in the tank to a nozzle 1 meter above the top of the tank is calculated by the integral 0 3' pg [14 x(12 2x)2dx O b' pg f14(12 2x)2(1 + x)dx O C) pg [25(12 2x)2(5 x)dx 0 d) pg f03 x(l2 2x)2dx O e) pg f; x(12 2x)2dx Assume the density of water is p km/m', and let the gravity of acceleration be g m/sec . The work, in Joules, needed to pump all the water in the tank to a nozzle 1 meter above the top of the tank is calculated by the integral Oa pg Ji x(12 - 2x)2 dx Ob) pg fi ( 12 - 2x )2 (1 + x) dx Od pg 1 ( 12 - 2x ) 2(5 - x) dx Od pg /o' x( 12 - 2x)2dx Oe pg / x(12 - 2x)2dx Of p8 > ( 12 - 2x ) 2 ( 2 + x ) dx