Question

35. Calculate the volume of a regular octahedron whose edges are
all 10 cm.​

Answer 1

Answer:

471.4cm³

Step-by-step explanation:

V≈471.4cm³

a Edge

10

cm

Answer 2

if cut in two, the octahedron can become a square based pyramid, with sides 10

volume of pyramid = (1/3) base area x height

diagonally across base, diagonal length = sqrt(10^2 + 10^2) = √200

then there is an isosceles triangle with base √200 and sides 10

so by pythagoras, height = √(10^2 - ((1/2)√200)^2 ) = √(100 -200/4) = √50

pyramid volume = (1/3) 100 x √50

total volume = 2 x pyramid = (2/3) x 100 x √50 = (1000 √2)/3

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