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uysha [10]
3 years ago
11

Find the volume of a cone with a height of 6 in and a base radius of 4 in

Mathematics
2 answers:
olga2289 [7]3 years ago
8 0

<u>Solution</u><u> </u><u>:</u><u>-</u>

Given :

  • Height of cone is 6 in.
  • Radius of base is 4 in .

To Find :

  • The Volume of come .

Now , we can find Volume of cone as ,

\boxed{\red{\bf{\dag Volume_{cone}=\dfrac{1}{3}\pi (radius)^2\times height }}}

\tt:\implies Volume_{cone} =\dfrac{1}{3}\pi r^2h

\tt:\implies Volume_{cone} =\dfrac{1}{3}\bigg\lgroup \dfrac{22}{7}\times 4^2\times 6\bigg\rgroup

\tt:\implies Volume_{cone} =\dfrac{1}{3}\times\bigg\lgroup \dfrac{22\times16\times6}{7}\bigg\rgroup

\tt:\implies Volume_{cone} =\dfrac{1}{3}\times 301 .71

\underline{\boxed{\red{\tt\longmapsto Volume_{cone}=100.571in^3}}}

\underline{\boxed{\green{\bf{\pink{\dag}Hence\:the\: Volume\:of\:cone\:is\:100.571in^3}}}}

Neko [114]3 years ago
5 0

Answer:

The answer is

<h2>100.5 in³</h2>

Step-by-step explanation:

The volume of a cone is given by

V  =  \frac{1}{3} \pi {r}^{2} h

where

r is the radius

h is the height of the cone

From the question

h = 6 in

r = 4 in

The volume of the cone is

V  =  \frac{1}{3}  \times  {4}^{2}  \times 6\pi \\  =  \frac{1}{3}  \times 16 \times 6\pi \\  =  \frac{1}{3}  \times 96\pi \\  = 32\pi \\  = 100.530964

We have the final answer as

100.5 in³

Hope this helps you

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Answer:

A. 4".

B. Approximately 9.54".

C. Approximately 13.54".

Step-by-step explanation:

Please find the attachment.

Let x be the distance from the peak of the kite to the intersection of the diagonals and y be the distance from the peak of the kite to the intersection of the diagonals.

We have been given that two sides of a kite are 10 inches and two sides are 5 inches. The shorter diagonal is 6 inches.

A. Since we know that the diagonals of a kite are perpendicular and one diagonal (the main diagonal) is the perpendicular bisector of the shorter diagonal.

We can see from our attachment that point O is the intersection of both diagonals. In triangle AOD the side length AD will be hypotenuse and side length DO will be one leg.

We can find the value of x using Pythagorean theorem as:

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Since distance can not be negative, therefore, the distance from the peak of the kite to the intersection of the diagonals is 4 inches.

B. We can see from our attachment that point O is the intersection of both diagonals. In triangle DOC the side length DC will be hypotenuse and side length DO will be one leg.

We can find the value of y using Pythagorean theorem as:

(OC)^2=(DC)^2-(DO)^2

Upon substituting our given values we will get,

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Upon taking square root of both sides of our equation we will get,

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\text{The length of the longer diagonal}=4+9.54

\text{The length of the longer diagonal}=13.54

Therefore, the length of longer diagonal is approximately 13.54 inches.

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