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3 years ago

This diagram shows a circle with an inscribed right triangle and some of its measurements in units.

Mathematics

1 answer:

Bumek [7]3 years ago

6 0

Answer:

Step-by-step explanation:

the hypotenuse of the right triangle is the diameter d of the circle

Using Pythagoras' identity in the right triangle

d² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )

d = $\sqrt{100}$ = 10

the circumference (C) of a circle is calculated as

C = πd = π × 10 = 10π

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Find the missing lengths: <br> HI=7 and LH=9, find LK.

Katarina [22]

Answer:

LK=12

Step-by-step explanation:

From the given figure, HI=7 and LH=9, and we know that

$(KH)^{2}=(IH)(HL)$

$(KH)^{2}=7{\times}9$

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Now, from ΔKHL, we have

$(OH)^{2}=(OK)(OL)$

and from ΔOKH,

$(KH)^{2}=(OH)^{2}+(OK)^2$

$(OK)^2=(KH)^2-(OH)^2$

$(OK)^2=63-(OK)(OL)$

$(OK)^2+(OK)(OL)=63$

$OK(OK+OL)=63$

$OK(KL)=63$ (2)

Also, ΔIKL is similar to ΔOHL, therefore

$\frac{OL}{KL}=\frac{9}{16}$

$\frac{KL-OK}{KL}=\frac{9}{16}$

$1-\frac{OK}{KL}=\frac{9}{16}$

$\frac{7}{16}=\frac{OK}{KL}$

Using equation (2), we get

$\frac{7}{16}=\frac{63}{(KL)^2}$

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Thus, the value of LK is 12.

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4 years ago

A cone is inverted and filled with water to of its height. What percent of the cone's volume is filled with water

wlad13 [49]

The 75% of the cone's volume is filled with water.

According to the statement

we have to find that the What percent of the cone's volume is filled with water.

So, For this purpose, we know that the

Cone is the surface traced by a moving straight line that always passes through a fixed point (the vertex).

So, Form given information

Let's call the height of the cone " h " and the area of its base " a ".

volume of cone = (1/3)(a)(h)

The water will also be in the shape of a cone, with a height that is 3/4 that of the container.

volume of water = (1/3)(a)(3/4 * h)

volume of water = (3/4) * (1/3)(a)(h)

volume of water = (3/4) * volume of cone

volume of water = 75% of the volume of cone

So, 75% of the cone's volume is filled with water.

Learn more about cone's volume here

brainly.com/question/1082469

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Question:

A cone is inverted and filled with water to 3/4 of its height. What percent of the cone's volume is filled with water?

#SPJ4

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