Chapter 12.5, Problem 27IP

a)

To determine

To find: volume of shown figure.

Answer to Problem 27IP

  $42c{m}^3$

Explanation of Solution

Given information: the given figure is

  

Formula used:

Volume = $l\times b\times h$

Calculation:

  $Volume=(7\times 2\times 3)=42c{m}^3$

b)

To determine

To find: volume change if one of dimensions two of dimension or three dimensions is doubled Explain.

Answer to Problem 27IP

Two times, four times and 8 times the original volume.

Explanation of Solution

Given information: the given expression is length, l=700m, width, b =2cm, height, h=3cm.

Formula used:

Volume = $l\times b\times h=v$

Calculation:

One of dimensions is doubled, let l, then volume, $v_1=2l\times b\times h=2(lbh)=2v$

Volume is doubled.

Two of dimensions are doubled, let l and b,

Then volume, $v_2=2l\times 2b\times h=4lbh=4v$ ,

Volume is 4 times.

Three of dimensions are doubled, let l, b and h,

Then volume, $v_3=2l\times 2b\times 2h=8lbh=8v$ v

Volume is 8 times then original.

c)

To determine

To find: charge in volume if each dimensions get triple.

Answer to Problem 27IP

27 times then original volume.

Explanation of Solution

Given information: the given expression is l=7cm, b=2cm, h=3cm.

Formula used:

V= $l\times b\times h$

Calculation:

Each dimension is triple

  $\begin{array}{l}l=3\times 7=21cm,b=2\times 3=6cm,h=3\times 3=9cm.\\ now,v=21\times 6\times 9=1134c{m}^3\end{array}$

1134 is 27 times original volume.

  $45\times 27=1134c{m}^3$

d)

To determine

To find: How volume of prism changes if each of the dimension is 6 time original.

Answer to Problem 27IP

216 times original volume

Explanation of Solution

Given information: the given expression is originally, l=7cm, b=2cm, h=3cm.

Formula used:

V= $l\times b\times h$

Calculation:

Volume will change 216 times

I.e. 6³ times since each sided changes to 6 times.