Solid Geometry

**sruthi07** · 12-19-2006, 05:54 PM

1.Three cubes of sides’ 1cm, 6cm and 8cm are merged into one cube without leaving any space. What is the length of side of new cube? Also its surface area

2. The volume of a box with a square base is 128cc. The height of the box is twice the breadth of the box. Find the height?

3.A road roller of diameter 3.5 m has to press a ground of area 1100sq meter. How many revolutions should it make?

4. Find the volume of the cube if the area of one of the faces is 81sqm?

5.If a cylindrical tank of diameter 14cm and of height 9cmis to be filled by water to 2/3rd of its height then what is the volume of the cylinder that is left empty?

6.Three cylindrical tanks of diameters 2m, 4m and 8m and of same height are to be filled simultaneously. What is the ratio of time taken in which they are filled?

**moe** · 12-19-2006, 06:19 PM

(1) wow! can i desintegrate the 6 and 8 sided cube in cubes of 1?!

(2) call breadth and width 's' and height '2s' ==> 2s*s*s=128 => s^3=64 => s=4 => height=2*4=8

(6) is the answer 1:2:4?

**een** · 12-20-2006, 03:30 AM

Hello, sruthi07!
Q1.Three cubes of sides’ 1cm, 6cm and 8cm are merged into one cube without leaving any space. What is the length of side of new cube? Also its surface area

1) Consider Three cubes of sides’ 1cm, 6cm and 8cm, hence if it will be merged into one cube without leaving any space the volume of new cube equals V=V1+V2+V3,
here V1- the volume of cube of side 1cm
V2- the volume of cube of side 6cm
V3- the volume of cube of side 8cm,
so V1=1
V2=216
V3=512,
V=729=d*d*d (by definition of cube's volume), d is the side of new cube, hence
d=9 cm,
2)Surface area of cube.
The square of one square (with side d=9cm) =81,
there are 6 squares, so surface area = 81*6=486
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Q2. The volume of a box with a square base is 128cc. The height of the box is twice the breadth of the box. Find the height?

the height=8
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Q3.A road roller of diameter 3.5 m has to press a ground of area 1100sq meter. How many revolutions should it make?

It is not clear for me, because if it is asked about the number or revolutions, IMHO we need know the lenght of all road.
So we can consider a road roller it is a cylinder with r=d/2, and we can find the lenght of cylinser's base is s1=2*pi*r.
At last the number of revolutions is (the lenght of all road)/s1.

What is the answer to this question?

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Q4. Find the volume of the cube if the area of one of the faces is 81sqm?

1) the area of one of the faces is S=81=a*a, here a is the length of square's side, so
a=9
2) the volume of the cube V=a*a*a, V=729
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Q5.If a cylindrical tank of diameter 14cm and of height 9cmis to be filled by water to 2/3rd of its height then what is the volume of the cylinder that is left empty?

1)Let's consider a cylindrical tank of diameter 14cm, so
the radius r is 7 cm
2) The total volume V=V1+V2, here V1 is volume of the cylinder that is left empty and V2-is volume of the cylinder with water.
Hence V1=V-V2
3)The total volume V=pi*r*r*H, r=7cm, H=9cm,
V2=pi*r*r*H1, H1=2/3 H
4)V1=V-V2=pi*r*r*H-pi*r*r*H1=pi*r*r*(H-2/3H)=1/3*pi*r*r*H
V1=1/3*pi*r*r*H=1/3*7*7*9*3.14 aprox 461.58
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All the best,
een

**een** · 12-20-2006, 04:09 AM

Originally Posted by moe

(1) wow! can i desintegrate the 6 and 8 sided cube in cubes of 1?!

(2) call breadth and width 's' and height '2s' ==> 2s*s*s=128 => s^3=64 => s=4 => height=2*4=8

(6) is the answer 1:2:4?

Hi, moe!

About Q6, to my mind the answer is 1:4:16.
6.Three cylindrical tanks of diameters 2m, 4m and 8m and of same height are to be filled simultaneously. What is the ratio of time taken in which they are filled?

1)Because we need consider volumes of cylindrical tanks.
The volume of cylinder is V=pi*(r^2)*H=pi*r*r*H, here r- radius of cylinder and H is the height,
r1=1m,r2=2m,r3=4m for 3 cylindres
so V1=pi*r1*r1*H,
V2=pi*r2*r2*H
V3=pi*r3*r3*H,
at last the time of filling t1=V1/v, t2=V2/v, t3=V3/v, v is the rate of filling,
t1:t3:t3=V1:V2:V3=1:4:16.

Regards,
een

**moe** · 12-20-2006, 08:47 AM

thank uuu!!!

**gre_girl** · 12-20-2006, 01:51 PM

hey een
thanks.

**KBTA** · 08-06-2007, 01:55 AM

Q5.If a cylindrical tank of diameter 14cm and of height 9cmis to be filled by water to 2/3rd of its height then what is the volume of the cylinder that is left empty?

1)Let's consider a cylindrical tank of diameter 14cm, so
the radius r is 7 cm
2) The total volume V=V1+V2, here V1 is volume of the cylinder that is left empty and V2-is volume of the cylinder with water.
Hence V1=V-V2
3)The total volume V=pi*r*r*H, r=7cm, H=9cm,
V2=pi*r*r*H1, H1=2/3 H
4)V1=V-V2=pi*r*r*H-pi*r*r*H1=pi*r*r*(H-2/3H)=1/3*pi*r*r*H
V1=1/3*pi*r*r*H=1/3*7*7*9*3.14 aprox 461.58

Empty Cylinder He=9*(1-2/3)=9*1/3=3
Empty volm= pi*7*7*3=147*pi=461.58

**KBTA** · 08-06-2007, 02:10 AM

Q6. Same to een
t1:t2=volm1/volm2
t1:t2=1:4
t2:t3=1/4=4/16
Combining those above,
t1:t2:t3=1:4:16

**rajneelam** · 08-09-2007, 02:22 PM

Kindly solve question 3 as am not able to do so

**rajneelam** · 08-09-2007, 02:40 PM

And alos for question 5 my ans is 462,everything is same as KBTA butt if you put 22/7 instead of pi you can cancel one 7 the resulet willl be 22*7*3=462.If we put decimal value of pi it cames 461.5 and putting fractional valve of pi it comes 462.