This question is incomplete because it lacks the required diagram. Please find attached the diagram required to answer the question.
Answer:
14 feet
Step-by-step explanation:
The volume of a cone = 1/3 πr²h
In the above question, we are given the volume = 314 cubic feet
the height is given in the attached diagram = 6ft
Step 1
We find the radius.
From the formula for the volume of a cone, we can derive the formula for radius of the cone.
Radius of the cone = √(3 × V/π × h
π = 3.14
Radius of the cone = √( 3 × 314 /3.14 × 6
Radius of the cone = √942/3.14× 6
Radius = √50
= 7.0710678119feet
Step 2
Diameter of the cone = Radius of the cone × 2
= 7.0710678119 × 2
= 14.142135624 feet
Approximately to the nearest foot = 14 feet
Therefore, the diameter of the cone to the nearest foot = 14 feet.
By definition, the perimeter of a square is given by:
Where,
L: length of the sides of the square.
When the sides of the square are tripled, the equation changes as follows:
Then, rewriting the equation we have:
Where,
P: perimeter of the original square.
Therefore, we can conclude that the perimeter is tripled.
Answer:
The perimeter of the square is tripled.
For a better understanding of the solution, please follow the diagram in the attached file.
A regular quadrilateral is basically a square.
So, if the base of the prism has a perimeter of 60 cm, then the length of the side of the square will be . It is shown of the diagram.
Now, from the diagram, it is clear that the lateral face area, which is given as 105 cm^2, is the product of the side of the square, which is known, and the unknown height, let us call it h. Thus, we will get the following equation:
This is depicted on the diagram.
Now, all our required parameters are in place. Thus, let us find what has been asked.
<u>SURFACE AREA</u>
Surface Area (SA) will be the sum of the areas of the two bases (squares) and the areas of the four lateral faces.
Since the side of one square base is 15 cm, therefore, the area of one square base will be .
Likewise, the area of one lateral surface is actually the area of a rectangle with length 15 cm and height 7 cm. Thus, it's area will be given as: .
Thus, our equation will be:
Therefore, Surface Area=870 cm^2
<u>VOLUME OF THE PRISM</u>
The volume of the prism will simply be the area of the base times the height of the prism.
Thus, the volume is:
