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

The formula p=8n-30 gives the profit p when a number of items n are each sold at $8 and expenses totaling $30 dollars are subtra

andrew11 [14]

Answer:

the answers is n=25. hope this helps

7 0

3 years ago

The distance between Capeton and Jonesville is 80 miles. The scale on the map is 0.75 in. : 10 miles. How far apart are the citi

Mnenie [13.5K]

The answer to this question is 6 in. Hope this helps.

7 0

3 years ago

A student raises her grade average from a 75 to a 90. What was the percent of increase in the student’s grade average? Round you

Zigmanuir [339]

=(new-old)/old *100%
=(90-75)/75 *100%
=20%
 hope it helps

5 0

3 years ago

Can someone solve this? and tell me how?

maksim [4K]

Answer:

1/3

Step-by-step explanation:

When working with balanced expressions (stuff on both sides of the equal sign), "what you do to one side, you do to the other", which keeps it balanced.

The first thing we notice is the exponent 1/4, which is one both sides, so we can get rid of it on both sides by using the reverse operation.

The reverse of exponents is square root.

$(4x + 10)^{\frac{1}{4}} = (9 + 7x)^{\frac{1}{4}}\\\sqrt[\frac{1}{4}]{(4x + 10)^{\frac{1}{4}}} = \sqrt[\frac{1}{4}]{(9 + 7x)^{\frac{1}{4}}}\\\\4x + 10 = 9 + 7x$

Isolate x to solve. Separate the variables and non-variables.

4x + 10 = 9 + 7x

4x - 4x + 10 = 9 + 7x - 4x Subtract 4x from both sides

10 = 9 + 3x

10 - 9 = 9 - 9 + 3x Subtract 9 from both sides

1 = 3x Divide both sides by 3 to isolate x

x = 1/3 Answer

8 0

3 years ago

You have a balance of $4,000 on your credit card with a 12% interest rate (1% per month). You plan to make no new purchases with

Alex787 [66]

Should be around $335-$340 per month

4 0

3 years ago