Find the volume of 20m, 5m, 18m

Mathematics

1 answer:

HACTEHA [7]1 year ago

7 0

Answer:

600 m³

Step-by-step explanation:

The shape we have is a rectangular pyramid:

Formula:<u><em> (volume of a rectangular pyramid)</em></u>

Volume = (1/3) × Base Area × height

___________________________

In our case :

Base area = L × W = 20 × 18 = 360 m²

height = 5 m

⇒ Volume = (1/3) × Base Area × height

$\Longrightarrow \text{volume} \ =\ \frac{1}{3} \times 360\times 5$

$\Longrightarrow \ \text{volume} \ =\ 600\ m^{3}$

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The position s(t) of a robot moving along a track at time t is given by s(t)=9t^2−90t+4.

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The total distance traveled by the robot from t=0 to t=9 is 1422 units

Integration is a way in which smaller components are brought together in pieces to form a whole. Integration can be used in finding areas, volumes and so on.

Given that the position s(t) at any time t is given by the function:

s(t)=9t²−90t+4

The total distance traveled by the robot from t=0 to t=9 can be gotten by integrating the position function within the limits 0< t < 9

Therefore:

$Total\ distance = \int\limits^9_0 {s(t) \, dt \\\\Total\ distance = \int\limits^9_0 {(9t^2-90t+4) \, dt\\\\Total\ distance = [3t^3-45t+4t]_0^9\\\\Total\ distance=-1422\ units$