Answer:
Refer to the attached file
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1 answer:
Answer:
314 m³
Step-by-step explanation:
The volume (V) of a cone is calculated using the formula
V = πr²h
where r is the radius and h the perpendicular height
To find h use the right triangle from the vertex to the midpoint of the base and the radius.
Using Pythagoras' identity on the right triangle
where the slant height is the hypotenuse, then
h² + 5² = 13²
h² + 25 = 169 ( subtract 25 from both sides )
h² = 144 ( take the square root of both sides )
h = = 12, hence
V = π × 5² × 12
= π × 25 × 4 = 100π ≈ 314 m³
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The question is related to application of derivatives .
Let A represents the area and s represent the side length .
Differentiating both sides with respect to t
It is given that ds/dt = 4cm/s
Substituting the values of s, ds/dt and on multiplying them, we will get
dA/dt = 2(5)(4) = 40 cm^2/s
Therefore rate of change of area when area= and rate of change of side is 4 cm/s is 40