Help with Geometry: Volume, Area and Perimeter of Pyramid

[beh4R]

Hello .
I am in the end of my exams and i have to do a geometry figure like a pyramid ( view image ) below
Now i should find the Perimeter, Volume and Surface of this figure .
Lengths are all 5 cm, Can somebody find and write the
Permiter,volume and surface for this figure please it's urgent

 

[earboth]

Hello .
I am in the end of my exams and i have to do a geometry figure like a pyramid ( view image ) below
Now i should find the Perimeter, Volume and Surface of this figure .
Lengths are all 5 cm, Can somebody find and write the
Permiter,volume and surface for this figure please it's urgent

Good morning,

I've to do a lot of guessing, so if I guessed correctly you can finish the problem, otherwise you have to provide us with additional detailed informations:

1. I assume that the figure shows a sector of a circle. If so the figure is the curved surface of a cone with the slanted line s = 5 cm and the arc a = 5 cm.
2. The area \(\displaystyle A_s\) of a sector is calculated by: \(\displaystyle A_s = \frac12 \cdot a \cdot s\)
3. The arc of the sector is the circumference of the base circle of the cone. You can determine the radius r of the base circle by: \(\displaystyle a = 2 \pi \cdot r\)
4. The volume of a cone is calculated by: \(\displaystyle V = \frac13 \cdot \pi \cdot r^2 \cdot h\)
where h denotes the height of the cone.
5. Use Pythagorean theorem to derive h from r and s.

I'll leave it to you to calculate the complete surface area of the cone.

... and btw I couldn't imagine what a perimeter of a solid could be?

 

[soroban]

Hello, beh4R!

I am in the end of my exams and i have to do a geometry
figure like a pyramid. .All lengths are 5 cm.

Find the perimeter, volume, and surface area.

            *
           * * * 5
        5 *   *   *
         *     *     *
        *       *   *
       *         * * 5
      *  *  *  *  *
            5

I assume this is a pyramid with a square base.There are four slanted edges of length 5.
The base is a square with side 5.
The perimeter is: $$4\cdot5 + 4\cdot 5 \:=\:40\:cm.$$

There are four equilateral triangles with side 5.
. . Their area is: $$4\cdot\tfrac{\sqrt{3}}{4}(5^2) \,=\,25\sqrt{3}\,cm^2$$
The base is a square with side 5.
. . Its area is $$5^2\,=\,25\,cm^2$$
Surface area: .$$(25\sqrt{3} + 25)\,cm^2$$

Slice the pyramid through two opposite slanted sides.

[SIZE=2]            *[/SIZE]
[SIZE=2]        5 * : * 5
        *   :   *
      *  *  *_ *  *
           5√2[/SIZE]

We have an isosceles right triangle.
Its height is $$\tfrac{5}{\sqrt{2}}\,cm.$$

Volume: .$$\tfrac{1}{3}(5^2)\left(\tfrac{5}{\sqrt{2}}\right) \:=\:\frac{125}{3\sqrt{2}}\,cm^3$$

 

[beh4R]

Hello, beh4R!


I assume this is a pyramid with a square base.There are four slanted edges of length 5.
The base is a square with side 5.
The perimeter is: $$4\cdot5 + 4\cdot 5 \:=\:40\:cm.$$

There are four equilateral triangles with side 5.
. . Their area is: $$4\cdot\tfrac{\sqrt{3}}{4}(5^2) \,=\,25\sqrt{3}\,cm^2$$
The base is a square with side 5.
. . Its area is $$5^2\,=\,25\,cm^2$$
Surface area: .$$(25\sqrt{3} + 25)\,cm^2$$

Slice the pyramid through two opposite slanted sides.

[SIZE=2]            *[/SIZE]
[SIZE=2]        5 * : * 5
        *   :   *
      *  *  *_ *  *
           5√2[/SIZE]

We have an isosceles right triangle.
Its height is $$\tfrac{5}{\sqrt{2}}\,cm.$$

Volume: .$$\tfrac{1}{3}(5^2)\left(\tfrac{5}{\sqrt{2}}\right) \:=\:\frac{125}{3\sqrt{2}}\,cm^3$$

ok thnaks so much i will write this in my notebook . hope its correct and to not remain in exam :) God bless you (Inlove)

 

[CellCoree]

Hello,

Sure, I would be happy to help you with finding the perimeter, volume, and surface area of a pyramid.

First, let's start with the perimeter. The perimeter of a pyramid is the sum of the lengths of all its sides. Since all the lengths in this pyramid are 5 cm, the perimeter would be 4 x 5 cm = 20 cm.

Next, let's calculate the volume. The volume of a pyramid is given by the formula V = (1/3) x base area x height. Since the base of this pyramid is a square with side length 5 cm, the base area would be 5 cm x 5 cm = 25 cm². The height of the pyramid can be calculated using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the height (h) is the hypotenuse and the other two sides (a and b) are the base and the slant height (l) of the pyramid. So, we can write the equation as h² = 5² + l². Since we know that the slant height of a pyramid is given by l = √(h² - (1/2b)²), we can substitute this in the equation and solve for h. After substituting and solving, we get h = √(25 - 12.5) = √12.5 ≈ 3.54 cm. Therefore, the volume of the pyramid would be V = (1/3) x 25 cm² x 3.54 cm ≈ 29.5 cm³.

Lastly, let's find the surface area. The surface area of a pyramid is given by the formula A = base area + (1/2) x perimeter x slant height. Again, the base area is 25 cm² and the perimeter is 20 cm. The slant height can be calculated using the Pythagorean theorem as mentioned earlier, so we get l = √(12.5 + (1/4) x 5²) = √(12.5 + 6.25) ≈ √18.75 ≈ 4.33 cm. Therefore, the surface area of the pyramid would be