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Marianna [84]
3 years ago
8

the volume of the a sphere whoes diameter is 18 cm is cubic cm . if it's diameter were reduced by half, it's volume would be of

its original volume
Mathematics
1 answer:
FrozenT [24]3 years ago
4 0

Answer:

The new volume is 8 times smaller than the original volume

Step-by-step explanation:

we know that

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

Let

z-----> the scale factor

x ----> the volume of the reduced sphere

y ----> the volume of the original sphere

so

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

we have

z=1/2 ----> scale factor

substitute

(1/2)^{3}=\frac{x}{y}

(1/8)=\frac{x}{y}

x=\frac{y}{8}

therefore

The new volume is 8 times smaller than the original volume

Verify

The volume of the original sphere is

r=18/2=9\ cm ---> the radius is half the diameter

V=\frac{4}{3}\pi (9)^{3}=972\pi \ cm^{3}

the volume of the reduced sphere is

r=9/2=4.5\ cm ---> the radius is half the diameter

V=\frac{4}{3}\pi (4.5)^{3}=121.5\pi \ cm^{3}

Divide the volumes

972\pi \ cm^{3}/121.5\pi \ cm^{3}=8

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Identify the base in this statement:<br> 16% of 98 is 15.68
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3 years ago
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3 years ago
A cylinder with a height of 12 cm is inscribed in a sphere with a radius of 10 cm. Find the lateral area of the cylinder. Answer
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Answer:

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Step-by-step explanation:

Given that:

The height of the cylinder: 12 cm

The radius of the sphere : 10

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Answer:

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= -4

We change this to -4 x 1.5 and shows the answer as -6

But the question had 2 negative numbers already and the answer is just positive 6.

8 0
3 years ago
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