1. Solve for x. Show your solution and justify every step.
1 answer:
You might be interested in
The maximum length of the prism is highest length of the hexagonal prism
The maximum length of each prism is 8.0 cm
<h3>How to determine the maximum length of each prism?</h3>The surface area of the hexagonal prism is calculated using:
A = 6al + 33 a^2
Where:
a represents the edge length; a = 4 cm
l represents the length (or height) of the prism
The surface area costs $0.04 per square centimeter.
So, we have:
C = 0.04 * [6al + 33 a^2]
The maximum cost is $11.
So, the equation becomes
11 = 0.04 * [6al + 33 a^2]
Substitute 4 for a
11 = 0.04 * [6 * 4l + 33 * 4^2]
Evaluate the products and exponents
11 = 0.04 * [24l + 483]
Divide both sides by 0.04
275 = 24l + 483
Subtract 483 from both sides
24l = 275 - 483
Evaluate the difference
24l = 191.9
Divide both sides by 24
l = 8.0
Hence, the maximum length of each prism is 8.0 cm
Read more about surface areas at:
Note: The height of the room must be 3 m instead of 3 cm because 3 cm is too small and it cannot be the height of a room.
Given:
Perimeter of the floor of a room = 18 metre
Height of the room = 3 metre
To find:
The area of 4 walls of the room.
Solution:
We know that, the area of 4 walls of the room is the curved surface area of the cuboid room.
The curved surface area of the cuboid is
Where, h is height, l is length and b is breadth.
Perimeter of the rectangular base is 2(l+b). So,
Putting the given values, we get
Therefore, the area of 4 walls of the room is 54 sq. metres.