Question

Знайдіть площу поверхні та об'єм правильної піраміди в основі якої лежить квадрат з діагоналлю 6 см а бічне ребро = 5 см

Answer 1

Прости. Я не понимаю тебя и поэтому не могу написать ответ.

Answer 2

Calculating the Surface Area and Volume of a Pyramid

To find the surface area (S) and volume (V) of a pyramid with a square base and a diagonal of 6 cm, and a lateral edge of 5 cm, we can use the following formulas:

1. Surface Area (S): - The surface area of a pyramid with a square base can be calculated using the formula: S = s^2 + 2s√(s^2/4 + h^2) where s is the length of the base side and h is the height of the pyramid.

2. Volume (V): - The volume of a pyramid can be calculated using the formula: V = (1/3) * (Area of the base) * (Height) where the area of the base is the square of the base side.

Calculations

Using the given dimensions: - Base diagonal (d) = 6 cm - Lateral edge (l) = 5 cm

We can calculate the base side (s) and the height (h) of the pyramid using the given dimensions.

1. Calculating the Base Side (s): - The base side of the square base can be calculated using the formula: s = d/√2 where d is the diagonal of the square base.

- Substituting the given value of the diagonal (d = 6 cm): s = 6/√2 = 6/1.414 ≈ 4.243 cm

2. Calculating the Height (h): - The height of the pyramid can be calculated using the lateral edge (l) and the base side (s): h = √(l^2 - (s/2)^2) where l is the lateral edge and s is the base side.

- Substituting the given values of the lateral edge (l = 5 cm) and the base side (s = 4.243 cm): h = √(5^2 - (4.243/2)^2) ≈ √(25 - 8.998) ≈ √16.002 ≈ 4 cm

3. Calculating the Surface Area (S): - Substituting the calculated values of s and h into the surface area formula: S = 4.243^2 + 2*4.243*√(4.243^2/4 + 4^2) S ≈ 18 + 2*4.243*√(4.243^2/4 + 4^2) S ≈ 18 + 2*4.243*√(4.243^2 + 16) S ≈ 18 + 2*4.243*√(18 + 16) S ≈ 18 + 2*4.243*√(34) S ≈ 18 + 2*4.243*5.831 S ≈ 18 + 9.686 S ≈ 27.686 cm^2

4. Calculating the Volume (V): - Substituting the calculated value of s and h into the volume formula: V = (1/3) * 4.243^2 * 4 V ≈ (1/3) * 18 * 4 V ≈ 24 cm^3

Conclusion

Therefore, the surface area of the pyramid is approximately 27.686 cm^2 and the volume is approximately 24 cm^3.