Scenario : PLAY TENTS
A company makes play tents for children. They make them in the shape of cuboids and square-based pyramids. The top and side faces of the tents are made using tarpaulin cloth. N.
material is used for the base.
Cuboid tent
Pyramid tent
Question:1) The cuboid tent has a square base of side x metres and heighth metres.
hm
Xm
Xm
The company uses 8m² of material to make each cuboid tent. What is the volume V
of the cuboid tent?
4
b) =
C) = 4
b) = (
82)
NEXT
Answers
Given : Tent in the shape of cuboids . The top and side faces of the tents are made using tarpaulin cloth. The cuboid tent has a square base of side x metres and height h metres.
The company uses 8m² of material to make each cuboid tent
To find : maximum volume V of the cuboid tent
Solution:
The cuboid tent has a square base of side x metres and height h metres.
Surface area = 4 * xh + x²
4 * xh + x² = 8
=> h = (8 - x²)/4x
Volume V = x²h
= x² (8 - x²)/4x
= x (8 - x²)/4
= 2x - x³/4
dV/dx = 2 - 3x²/4
dV/dx = 0
2 - 3x²/4 = 0
=> x² = 8/3
=> x = 2√(2/3) m
d²V/dx² = -6x/4 < 0
Hence Volume is maximum when x = 2√(2/3)
h = (8 - x²)/4x = (8 - 8/3) /4(2√(2/3)) = (2/3) /√(2/3) = √(2/3)
=> h = √(2/3) m
Volume = x²h =( 8/3 ) √(2/3) = 8√2 / 3√3 m³
volume V of the cuboid tent = 8√2 / 3√3 m³
Learn More:
An open box is to be made from a square piece of material, 24 cm on
https://brainly.in/question/9492013
an open box made from a rectangular cardboard of sides 35cm and ...
https://brainly.in/question/7723556
A open box with a square base is to be made. Its total surface area is ...
https://brainly.in/question/11774623