Question 825040
1) {{{volume=(40cm)(20cm)(80cm)=40*20*80}}}{{{cm^3=40*20*2*40}}}{{{cm^3=40*20*2*40}}}{{{cm^3=40*40*40}}}{{{cm^3=(40cm)(40cm)(40cm)=(40cm)^3}}}
A cube of edge length {{{highlight(40cm)}}} has the same volume as the 40cm x 20cm x 80cm cuboid.
 
2) {{{343=7^3}}} so a cube with a volume of 343 cubic cm has an edge length of 7 cm.
Each face will have a surface area of
{{{(7cm)(7cm)=49}}} square cm,
and the total surface area of all 6 faces of the cube will be
{{{6*"( 49"}}}{{{square}}}{{{"cm )"=highlight(294)}}}{{{square}}}{{{cm}}} .
 
3) the volume of the tank, in cubic meters, is
{{{4*2*1.2=9.6}}}
A cubic meter is 1000 cubic decimeters, or 1000 liters.
A tank containing {{{9.6*1000L=9600L}}} can fill a {{{15L}}} bucket
{{{9600L/"15 L"=highlight(640)}}}{{{times}}}
 
4) For a cylinder,
{{{total}}}{{{area=lateral}}}{{{area+2*base}}}{{{area=462}}}{{{square}}}{{{cm}}}
{{{lateral}}}{{{surface}}}{{{area=2pi*radius*height=462/3}}}{{{square}}}{{{cm=154{{{square}}}{{{cm}}}
the remaining {{{462}}}{{{square}}}{{{cm-154}}}{{{square}}}{{{cm=308}}}{{{square}}}{{{cm}}} is the area of both bases.
The area of each base is {{{308/2}}}{{{square}}}{{{cm=154}}}{{{square}}}{{{cm}}}
{{{base}}}{{{area=pi*radius^2=154}}}{{{square}}}{{{cm}}}
{{{radius^2=154/pi}}}{{{square}}}{{{cm=49}}}{{{square}}}{{{cm}}} (rounded)
so {{{radius=sqrt(49cm^2)=highlight(7cm)}}}
Going back to the lateral area, and substituting {{{7cm}}} for {{{radius}}} in
{{{2pi*radius*height=154cm^2}}} we get
{{{2pi*(7cm)*height=154cm^2}}}
{{{height=154cm^2/(2pi*(7cm))=highlight(3.5cm)}}} (rounded)
So, {{{volume=base}}}{{{area*height=154cm^2*3.5cm=highlight(539cm^3)}}} (approximately).