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

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Reika [66]

Answer:

d = 5

Step-by-step explanation:

We want to know what d would be when x = -1, so we can start off by plugging in -1 for x to get the following equation: $\sqrt{8 - (-1)} = 2(-1)+d$ . On the left hand side, 2 negatives become a positive sign, so the -(-1) becomes a +1, and 8+1 would equal 9. On the right hand side, we just multiply 2 and -1 to get -2. So, the equation now looks like this: $\sqrt{9} = d-2$ . We know that $\sqrt{9}$ = 3, so we would get 3 = d-2. THen we would add 2 to both sides to get d = 5. Hope this helps!