A cuboidal pillar of dimensions 25 cm X 15 cm X 4 m and a cylindrical pillar of radius 14 cm and height 10 m are to be made for a project. Which of the pillars require more material and by how much?
Answers
✇ Given:-
▪︎Dimension of cuboidal pillar
= 25 cm × 15 cm × 4 m
= 25cm × 15cm × 400cm
▪︎Radius of cylindrical pillar = 14cm
▪︎Height of cylindrical pillar = 10m = 1000cm
════◄••❀••►════
✇ To Find:-
- Which pillar required more material?
- Material required by how much?
════◄••❀••►════
✇ Formula/Concept Used:-
- Volume of cuboid = l × b × h
- Volume of cylinder = πr²h
- Volume of material required more
= Volume of (Bigger pillar - Smaller pillar)
Here;
▪︎l = length
▪︎b = breadth
▪︎h = height
▪︎π = 22/7
▪︎r = radius
════◄••❀••►════
✇ Solution:-
➥ Finding volume of cuboidal pillar:
Volume of cuboidal pillar
= l × b × h
= 25 × 15 × 400
= 150000 cm³
Volume of cuboidal pillar is 150000cm³
┄┄╌╌╌╌┄┄┈┈┈─
➥ Finding volume of cylindrical pillar:
Volume of cylindrical pillar
= πr²h
= (22/7) × (14)² × 1000
= (22 × 196 × 1000) ÷ 7
= 4312000 ÷ 7
= 616000 cm³
Volume of cylindrical pillar is 616000 cm³
┄┄╌╌╌╌┄┄┈┈┈─
➥ Finding which pillar required more material:
As,
150000cm³ < 616000cm³
Hence,
Volume of cuboid < Volume of cylinder
So, here Volume of cuboidal pillar is required more material than volume of cylindrical pillar.
┄┄╌╌╌╌┄┄┈┈┈─
➥ Finding material required by how much:
Volume of material required more
= Volume of (Bigger pillar - Smaller pillar)
= Volume of ( cuboid- cylinder )
= 616000cm³- 150000cm³
= 466000 cm³
════◄••❀••►════
✇ Answer:-
Cylindrical pillar required more material than cuboidal pillar by 466000cm³ .