What is the volume of the cone shown below?

Mathematics

1 answer:

andrezito [222]2 years ago

8 0

<h3>Answer: Choice A) 1344π cubic units</h3>

Work Shown:

r = 8 = radius

h = 63 = height

V = volume of the cone

$V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*8^2*63\\\\V = \left(\frac{1}{3}*8^2*63\right)\pi\\\\V = \left(\frac{1}{3}*63*8^2\right)\pi\\\\V = \left(21*64\right)\pi\\\\V = 1344\pi\\\\$

Side note: You could write the symbol π as "pi" without quotes.

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HJ = 18 and MN = 28. Solve for LK

Brut [27]

Answer:

LK = 38

Step-by-step explanation:

MN is the midsegment, and the midsegment is the average length of the top and bottom, so:

$\frac{18 + LK}{2} =28$

solve for LK:

$18+LK=56\\\\LK=38$

5 0

3 years ago

an inverted cone has a height of 11 inches and an initial radius of 18 inches. the volume of the inverted cone is decreasing at

joja [24]

Radius of cone is decreasing at the rate of $\frac{1623}{110\pi}$ inches

What is rate of change?

Suppose there is a function and there are two quantities. If one quantity of a function changes, the rate at which other quantity of the function changes is called rate of change of a function.

Here rate of change of radius of cone has been calculated

Radius of cone = 18 inches

Height of cone = 11 inches

Volume of cone (V) = $\frac{1}{3} \pi r^2h$

$\frac{dV}{dt} = \frac{1}{3} \pi h (2r\frac{dr}{dt})\\-541 = \frac{2}{3} \pi \times 11\times 5\times\frac{dr}{dt}\\\frac{dr}{dt} = -\frac{541 \times 3}{2 \times \pi \times 11 \times 5}\\\frac{dr}{dt} = -\frac{1623}{110 \pi}$