All categories

3 years ago

A cone has a volume of 2560π cm cubed and a heigh of 30 cm.

Mathematics

1 answer:

Korolek [52]3 years ago

8 0

Answer:

r = 16 cm

g = 34 cm

LA = 1708.16 cm^2

Step-by-step explanation:

We have that for the cone, the formula is as follows:

v = pi / 3 * r ^ 2 * h

the first thing they ask is to calculate the radius, therefore we solve for r

r ^ 2 = 3 * v / (pi * h)

replacing the volume and height, it remains:

r ^ 2 = 3 * 2560 * pi / (pi * 30)

r ^ 2 = 3 * 2560/30 = 256

r = 16

Now, to calculate the slant height, that is to say g, we can calculate it knowing the height and the radius:

g ^ 2 = r ^ 2 + h ^ 2

g ^ 2 = 16 ^ 2 + 30 ^ 2

g ^ 2 = 1156

g = 34

The lateral area of the cone is given by the following equation:

LA = pi * r * g

replacing

LA = 3.14 * 16 * 34

LA = 1708.16 cm ^ 2

the lateral area is 1708.16 cm ^ 2

You might be interested in

Four times a number x is at least 16

Angelina_Jolie [31]

Answer:

Step-by-step explanation:

4x=16

x=4

7 0

3 years ago

Read 2 more answers

A group of 15 friends take a trip to a water park. The total price of the trip is $599.85 before any discounts. The total price

Citrus2011 [14]

Answer:10

Step-by-step explanation:

3 0

3 years ago

Express this to the nearest whole .

RSB [31]

Answer:

its 30 the a in thst problem is silents

Step-by-step explanation:

3 0

2 years ago

Ex 2.8<br> 3. find the maximum value of y for the curve y=x^5 -3 for -2≤x≤1

harkovskaia [24]

$y=x^5-3\\ y'=5x^4\\\\ 5x^4=0\\ x=0\\ 0\in [-2,1]\\\\ y''=20x^3\\\\
y''(0)=20\cdot0^3=0$

The value of the second derivative for $x=0$ is neither positive nor negative, so you can't tell whether this point is a minimum or a maximum. You need to check the values of the first derivative around the point.
But the value of $5x^4$ is always positive for $x\in\mathbb{R}\setminus \{0\}$ . That means at $x=0$ there's neither minimum nor maximum.
The maximum must be then at either of the endpoints of the interval $[-2,1]$ .
The function $y$ is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.

$y_{max}=y(1)=1^5-3=-2$

4 0

3 years ago

PLEASE HELP ME WITH THIS WILL GIVE 30 POINTS

maxonik [38]

Answer:

i think the area is 21 srry if im wrong

Step-by-step explanation:

8 0

3 years ago