MHB 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 $$A_s$$ of a sector is calculated by: $$A_s = \frac12 \cdot a \cdot s$$
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: $$a = 2 \pi \cdot r$$
4. The volume of a cone is calculated by: $$V = \frac13 \cdot \pi \cdot r^2 \cdot h$$
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.

            *
        5 * : * 5
        *   :   *
      *  *  *_ *  *
           5√2

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.

            *
        5 * : * 5
        *   :   *
      *  *  *_ *  *
           5√2

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)