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Allisa [31]
2 years ago
8

Volume of a cone = r²h,

Mathematics
1 answer:
inessss [21]2 years ago
6 0

Answer:

7.5 m           457.5\pi m^{2}

Step-by-step explanation:

First, visualize the original cone and the smaller cone as overlapping similar triangles. The scale factor of the original cone to the smaller cone is 50:40, so if the smaller cone has a radius of 6 m, then the radius of the original cone would be 7.5 m.

The volume of the frustum is the volume of the original cone minus the volume of the smaller cone. The formula for the volume of a cone is V = \frac{1}{3} \pi r^{2}h.

Original Cone = \frac{1}{3} \pi r^{2}h = \frac{1}{3} \pi *7.5^{2}*50 = 937.5\pi

Smaller Cone = \frac{1}{3} \pi r^{2}h =  \frac{1}{3} \pi *6^{2}*40 = 480\pi

Frustum = 937.5\pi - 480\pi = 457.5\pi

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2(17) + 2(6), which gives us 46, so the perimiter is 46.
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3 years ago
If (n+1)!=90×(n-1)!,find n.​
Helen [10]

 

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2 years ago
Work out the lengths of side a and side b 8cm and 5 cm 1 triangle 17cm and 12 cm on the other triangle pythagoras
Viktor [21]

Answer:

a = 9.4 cm

b = 12.0 cm

Step-by-step explanation:

Check the image uploaded for diagram;

For the first diagram, side length a is calculated as follows;

a² = 8²  +  5²

a² = 64  +  25

a² = 89

a = √89

a = 9.4 cm ( approximated to 1 decimal place)

For the second diagram, side length b is calculated as follows;

b² = 17²  -  12²

b² = 145

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b = 12.0 cm (approximated to 1 decimal place)

3 0
3 years ago
The height of one solid limestone square pyramid is 21 m. A similar solid limestone square pyramid has a height of 30 m. The vol
Elina [12.6K]

Answer:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form is \frac{7}{10}

Part b) The ratio of the volume of the smaller pyramid to the larger pyramid is \frac{343}{1,000}

Part c) The volume of the smaller pyramid is 4,116\ m^{3}

Step-by-step explanation:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

so

Let

z----> the scale factor

x----> the height of the smaller pyramid

y----> the height of the larger pyramid  

z=\frac{x}{y}

substitute the values

z=\frac{21}{30}

Simplify

z=\frac{7}{10} -----> scale factor in simplest form

Part b) Ratio of the volume of the smaller pyramid to the larger pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid  

z^{3}=\frac{x}{y}

we have

z=\frac{7}{10}

substitute

\frac{7}{10}^{3}=\frac{x}{y}

Rewrite

\frac{x}{y}=\frac{343}{1,000} -----> ratio of the volume of the smaller pyramid to the larger pyramid

Part c) The volume of the smaller pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid  

z^{3}=\frac{x}{y}

we have

z=\frac{7}{10}

y=12,000\ m^{3}

substitute the values and solve for x

(\frac{7}{10})^{3}=\frac{x}{12,000}

x=\frac{343}{1,000}(12,000)=4,116\ m^{3}

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The answer to this question would be x=a2y2
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