Question

11. A water tank is in the form of a sphere. It is filled with water to a depth of 30 cm. the inner diameter of the tank is 45 cm, what is the volume of water in it in liters? A.18.25 liters C 28.49 liters B. 21.61 liters D.35.34 liters 12. A rectangle ABCD is given such that AB is 5 units of measure while BC is 2 units. A solid is to be formed by rotating the rectangle around side AB. Determine its volume in square units A.61.23 cu units C 61.43 cu.units B.62.83 cu.units D. 65.46 cu.units 13. A 4.2 cm by 4.2 cm square pyramid with a lateral edge of 15cm. What is the volume? A. 89.44 B. 86.44 C. 44.98 D. 44.68 14. The perimeter of an ellipse is 28.448cm. The major axis is 10cm. long lies on the x-axis with its center at the origin. Determine the equation of the ellipse. A. 17x^2 +26y^2-500 = 0 C 19x^2 +25y^2 - 400 = 0 B. 16 x^2 +25y^2 - 400 = 0 D. 20x^2 + 26y^2 - 500 = 0 15. A corner lot is 30 m on the street and 20 m on the other street, the angle between the two lines on the street being 80°. The other two lines of the lot are perpendicular to the lines on the street. Determine the area of the lot. A. 495 B. 457 C. 347 D. 747 16. The axis of the cone makes an angle of 60 degrees with the horizontal. If the length of the axis is 30cm. and its base radius is 20cm., compute for the volume of the curve. A. 10992.5 cu.cm C10772.5 cu.cm B. 10882.5 cu.cm D. 10662.5 cu.cm 17. In a factory, there are 3 machines A, B and C. When all three are running, they produce 222 suitcases per day. If A and B work but C does not, they produce 159 suitcases per day. If B and C work but A does not, they produce 147 suitcases per day. What is the daily production of C? A. 45 B. 36 C. 63 D. 54 18. How many minutes after 3:00 pm will the hands of the clock be at 180°? A. 49.1 B. 45.6 C. 50.2 D. 46.7 19. How many seconds longer is 3% of an hour than is 20% of a minute? A. 80 B. 108 C 96 D. 88 20. The altitude of a regular cone is twice its base radius. If its volume is 3400 cu.cm. What is the total surface area A. 1404 m^2 B. 4567 m2 C. 1505 m^2 D.5678 m^2

anyone can help me to solve this all problems? thank you so much ?

Answer 1

11.

volume of unfilled portion of tank=

* pi*h? * (3r - h)

=

* 3.14 * 152 * 3 * 22.5 - 15)

=12370.02 $cm^{3}$

where h =height above head of water

r= radius of sphere

volume of sphere =
*pi*p3
=
*3.14 + 22.53
=47712.9$cm^3$

volume of water=volume of sphere -volume of unfilled portion=(47712.9-12370.02)=35342.8$cm^3$=35.34 l

(density of h2o=1000 litres/$m^3$=10^-3 l/$cm^3$)

12.as the rectangle is rotated around AB the new solid formed is a cylinder with AB as the height and BC as its radius

3.14*22*5

The volume of the solid =
pixp²h
=
3.14*22*5
=62.8 cu.units

13.diagnol of base square = =5.94

(4.22 +4.2):

height of pyramid= =14.7

+769291)

volume of pyramid=$a^2\frac{h}{3}$ =$4.2^2\frac{14.7}{3}$=86.44

17.let the production rate of A,B and C be x,y,z suitcases per day respectively

from given data

$x+y+z=222$ ....i

...ii

x + y = 159

$y+z=147$ ...iii

Substituting ii from i we get z=222-159=63

therefore c produce s 63 suitcases per day

18.49.1 mins

19. 3 percent of an hour=$\frac{3}{100}*60*60$ =108 seconds

20 percent of a minute=$\frac{20}{100}*60$=12 seconds

108-12=96 seconds

20.Given h=2r

Volume of regular cone=$\frac{pi}{3}*r^{2}*h$ =$\frac{3.14}{3}*r^{2}*2r$=2.093$r^3$=3400cu.cm

r=$3400^\frac{1}{3}$. =15.036

h=2*15.036