Directions: Study the following graph and answer the questions
The following bar graph shows the dimensions of cone, cylinder and sphere in cm.
Now 3 more 3D figure cube, prisms and pyramid notes are given Notes:
1. The length of the cube is similar with the diameter of the sphere
2. The height of prism is similar to the height of a cone.
3. The side of the prism is 3/5th the radius of the cone.
4. The height of the pyramid is similar with the radius of the sphere
5. The side of the pyramid is similar with 4/5th of height of the cylinder
* All figures are solid
* Base of the prism = square
* Base of the pyramid is equilateral triangle
1) Find the ratio of the volume of the cone to pyramid?
A. 54:53√(3)
B. 53:55√(3)
C. 57:54 √(3)
D. 165:28 √(3)
E. None of these
Sol:
The volume of the cone= 1/3 *22/7*r2*h
=1/3 *22/7* 102*18 cm3
The volume of pyramid
=1/3* area of base * height
=1/3 *√(3)/4 *162 *15 cm3
So the ratio will be
=> 1/3 *22/7*100*18:1/3*√(3)*64*15
= 165 :28 √(3)
2) Find the ratio of volume of cylinder to prism.
A. 12340:567
B. 14360:576
C. 14300:687
D. 14080:567
E. 15400:786
Sol:
The volume of the cylinder = 22/7 *162 *20cm3
Volume of the prism= area of base * height
As the area of the prisms is square
So area of the base= 6*6=36 cm2
So the volume= 36 *18 cm3
So the required ratio= 22/7*16*16*20:36*18
=14080:567
3) Find the difference between the total surfacearea of the sphere and cylinder?
A. 687 cm2
B. 753 cm2
C. 782 cm2
D. 792 cm2
E. 497 cm2
Sol:
The total surfacearea of the sphere= 4 *22/7
*15*15
=88*225/7=2828.57 cm2
The total area of the cylinder= perimeter of the
base *height+2* base area
=2*22/7*16*20 +2*22/7 *16*16
=22/7(640+512)
=22/7(1152)
=3620.57cm2
So, the required difference= 3620.57-
2828.57=792cm2
4) The total surfacearea of the cone is how much percent more or less than the total surfacearea of the cube?
A. 99.5% more
B. 95.4% less
C. 94.4% less
D. 97.6% less
E. 82.19% less
Sol:
The radius of the cone= 10cm, and the height of
the cone=18cm
So, the slant height= √(182+102)
=√(324+100) =√(424)=20.59cm
So, the totalsurface area of the cone=22/7
*10*20.6 +22/7 *10*10
=22/7(206+100)=22/7 *306=961.71 cm2
The total surface area of cube= 6* length *
length
=5400 cm2
So the required percentage=(5400-961.71)/5400
*100
=82.19% less
