SOLUTION: Please help me solve these with proper steps: 1.) the dimensions of a cuboid are 40cm x 20cm x 80cm.find the length of a cube (edge) which has the same volume. 2.) the volume

Algebra ->  Surface-area -> SOLUTION: Please help me solve these with proper steps: 1.) the dimensions of a cuboid are 40cm x 20cm x 80cm.find the length of a cube (edge) which has the same volume. 2.) the volume      Log On


   

Question 825040: Please help me solve these with proper steps:
1.) the dimensions of a cuboid are 40cm x 20cm x 80cm.find the length of a cube (edge) which has the same volume.
2.) the volume of a cube is 343 cubic cm.find its total surface area.
3.)how many buckets of capacity 15 litres can be filled from a tank 4m long,2m broad,1.2m high,full of water?
4.) a solid cylinder total surface area of 462 square cm.its curved surface area/lateral surface area is one third of its total surface area.find the volume.
Thank you.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
1) volume=%2840cm%29%2820cm%29%2880cm%29=40%2A20%2A80cm%5E3=40%2A20%2A2%2A40cm%5E3=40%2A20%2A2%2A40cm%5E3=40%2A40%2A40cm%5E3=%2840cm%29%2840cm%29%2840cm%29=%2840cm%29%5E3
A cube of edge length highlight%2840cm%29 has the same volume as the 40cm x 20cm x 80cm cuboid.

2) 343=7%5E3 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
%287cm%29%287cm%29=49 square cm,
and the total surface area of all 6 faces of the cube will be
6%2A%22%28+49%22square%22cm+%29%22=highlight%28294%29squarecm .

3) the volume of the tank, in cubic meters, is
4%2A2%2A1.2=9.6
A cubic meter is 1000 cubic decimeters, or 1000 liters.
A tank containing 9.6%2A1000L=9600L can fill a 15L bucket
9600L%2F%2215+L%22=highlight%28640%29times

4) For a cylinder,
totalarea=lateralarea%2B2%2Abasearea=462squarecm
lateralsurfacearea=2pi%2Aradius%2Aheight=462%2F3squarecm=154%7B%7B%7Bsquarecm
the remaining 462squarecm-154squarecm=308squarecm is the area of both bases.
The area of each base is 308%2F2squarecm=154squarecm
basearea=pi%2Aradius%5E2=154squarecm
radius%5E2=154%2Fpisquarecm=49squarecm (rounded)
so radius=sqrt%2849cm%5E2%29=highlight%287cm%29
Going back to the lateral area, and substituting 7cm for radius in
2pi%2Aradius%2Aheight=154cm%5E2 we get
2pi%2A%287cm%29%2Aheight=154cm%5E2
height=154cm%5E2%2F%282pi%2A%287cm%29%29=highlight%283.5cm%29 (rounded)
So, volume=basearea%2Aheight=154cm%5E2%2A3.5cm=highlight%28539cm%5E3%29 (approximately).