The volume is 1,570 ft3
67
Volume of the pyramid: 1/3*base area*height in cubic m
slant height of the pyramid Louvre in Paris=28 meters
Yes, the slant height of a regular square pyramid is longer than its altitude. The altitude is the perpendicular height from the apex to the center of the base, while the slant height is the distance from the apex to the midpoint of a side of the base. In a right triangle formed by the altitude, half the base side, and the slant height, the slant height serves as the hypotenuse, making it inherently longer than the altitude.
The surface area of the pyramid is superfluous to calculating the slant height as the slant height is the height of the triangular side of the pyramid which can be worked out using Pythagoras on the side lengths of the equilateral triangle: side² = height² + (½side)² → height² = side² - ¼side² → height² = (1 - ¼)side² → height² = ¾side² → height = (√3)/2 side → slant height = (√3)/2 × 9cm = 4.5 × √3 cm ≈ 7.8 cm. ---------------------------- However, the surface area can be used as a check: 140.4 cm² ÷ (½ × 9 cm × 7.8 cm) = 140.4 cm² ÷ 35.1 cm² = 4 So the pyramid comprises 4 equilateral triangles - one for the base and 3 for the sides; it is a tetrahedron.
V = 1,570 ft3
67
The slant height will be 25 cm
The volume of a regular pyramid with a square base of 8cm and a slant height of 5 cm is: 64 cm3
This pyramid would have a perpendicular height of 3, a volume of 64 units3 and a slant edge of 6.403
Volume of the pyramid: 1/3*base area*height in cubic m
To find the volume of a pyramid, you can use the formula ( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} ). For a pyramid with a square base of edge length ( W ), the base area is ( W^2 ). The height can be determined using the slant height and the properties of a right triangle; however, if the height is not given, the volume cannot be precisely calculated. Assuming you have the height ( h ), the volume would be ( V = \frac{1}{3} W^2 h ).
slant height of the pyramid Louvre in Paris=28 meters
The volume would be 1,500 m3
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The slant height of a pyramid is crucial for calculating the surface area and volume of the structure. It represents the distance from the apex of the pyramid to the midpoint of a base edge, which is essential for determining the area of the triangular faces. Additionally, knowing the slant height helps in practical applications, such as materials estimation for construction or design purposes, ensuring accurate and efficient project planning.
The height of the triangular face of a pyramid is called the slant height.