Volume of reg sq. pyramid = vp
vp = 1/3×s^2×h, where s = side and h = height
Volume of cone = vc =1/3×h×pi×r^2
Now we know that h is the same for both, and the cones diameter = s of square base, so radius (r) = 1/2 s
so now vc = 1/3×h×pi×(1/2s)^2
let's remove the same items for both vc and vp
so 1/3 and h
now let's plug an arbitrary number into each:
vc = pi (10/2)^2 = 3.14×25 = 78.54
vp = s^2 = 10^2 = 100
So any square pyramid has slightly more volume than the cone

4 0

2 years ago

Could i have some really really quick help?

nata0808 [166]

Answer:

1125 m

Step-by-step explanation:

Given equation:

$h=-5t^2+150t$

where:

h = height (in metres)
t = time (in seconds)

<u>Method 1</u>

Rewrite the equation in vertex form by completing the square:

$h=-5t^2+150t$

$\implies h=-5t^2+150t-1125+1125$

$\implies h=-5(t^2-30t+225)+1125$

$\implies h=-5(t-15)^2+1125$

The vertex (15, 1125) is the turning point of the parabola (minimum or maximum point). As the leading coefficient of the given equation is negative, the parabola opens downward, and so vertex is the maximum point. Therefore, the maximum height is the y-value of the vertex: 1125 metres.

<u>Method 2</u>

Differentiate the function:

$\implies \dfrac{dh}{dt}=-10t+150$