Ans: 3112mm^3
V = 1/3 base area x height
Base area is 23 x 23 = 529
(it's a square)
Find the diagonal of the base first & half it, giving you the mid-point of the square from bottom to the top of the shape or the vertex.
a^2 + b^2 = c^2
23^2 + 23^2 = c^2
Square root
C = root 23^2 + 23^2
Then, divide by 2 to get half of the length
root 23^2 + 23^2 / 2 = 23root2/2
Or
16.27 to 2d.p
Create a right-angle triangle & use Pythagoras Theorem again:
Dimensions of 16.27 (base) & 24mm (hypotenuse) given above. So, missing side/length is the height.
Rearrange equation: (a^2 + b^2 = c^2)
C^2 - b^2 = a^2
(doesn't matter where a & b is, it'll also give u the same answer)
24^2 - 16.27^2 = a^2
Square root
a = root 24^2 - 16.27^2
a = 17.65 to 2d.p
H=17.65 to 2d.p
V = 1/3 base area x height
= 1/3 x 529 x 17.65
= 3112.283333
= 3112.28 to 2d.p
(but, v=3112.170938mm^3 when I use exact value of the height)
Volume = 3112.17mm^3 to 2d.p
Or 3112mm^3 to 4 s.f. (as our integer)
(used exact value of numbers - in my calculation)
Hope this helps!
