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3 years ago

A cone with a radius of 3" has a total area of 24π sq. in. Find the volume of the cone.

2 answers:

5 0

The answer is 12π.

To get the volume of the cone, we need the height. The radius is given.

V = πr² × (h/3)

The total surface area of the cone is:
SA = πr² + πrl where r is radius and l is slant height

24π = π(3)² + π(3)(l)
24π = 9π + 3πl
24π - 9π = 3πl
15π = 3πl
l = 15π / 3π
l = 5

Using Phytagoras, we can calculate the height of the cone:
l² = h² + r²
5² = h² + 3²
25 - 9 = h²
h = √16
h = 4

Therefore the volume is:
V = π(3)² × (4 / 3)
V = 3π × 4
V = 12π

Kobotan [32]3 years ago

3 0

The volume of the cone is: 12 pi

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Plz explain it to me? and answer

Viefleur [7K]

The question states that both parts of Noshi's desk were shaped like trapezoids and both had a height of 3.

We know that the formula for area of a trapezoid is (a+b)/2 * h, where a and b are bases of the trapezoid and h is the height. Note: This is like any other form of trying to find the area, because we are doing base times height, however, we need to divide the sum of the bases by 2 to find the average base length.

Let's call the first trapezoid on the left Trapezoid A and the second slanted trapezoid Trapezoid B.

Area of Trapezoid A = (a+b)/2 * h = (5+8)/2 * 3 = 13/2 * 3 = 6.5 * 3 = 19.5 feet
Area of Trapezoid B = (a+b)/2 * h = (4+9)/2 * 3 = 13/2 * 3 = 6.5 * 3 = 19.5 feet

To find the area of Noshi's total desk, we simply need to add the areas of Trapezoid A and Trapezoid B together.

19.5 feet + 19.5 feet = 39 feet

Therefore, the area of Noshi's desk is 39 feet.

Hope this helps! :)

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3 years ago

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3 years ago

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Step-by-step explanation:

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3 years ago

The 2 main support rods for a barbeque grill are each 7.5 cm from the centre of the

sukhopar [10]

Answer:

58.1 cm

Step-by-step explanation:

The length of each support rod can be found using the Pythagorean theorem. The geometry can be modeled by a right triangle, such that the distance from centre is one leg and half the length of the rod is the other leg of a triangle with hypotenuse equal to the radius of the grill.

<h3>Pythagorean theorem</h3>

The theorem tells us that the sum of the squares of the legs of a right triangle is the square of the hypotenuse. For legs a, b and hypotenuse c, this is ...

c² = a² +b²

<h3>application</h3>

For the geometry of the grill, we can define a=7.5 and c=30. Then b will be half the length of the support rod.

30² = 7.5 +b²

b² = 900 -56.25 = 843.75

b = √843.75 ≈ 29.0473

The length of each support rod is twice this value, so ...

rod length = 2b = 2(29.0473) = 58.0947

Each support rod is about 58.1 cm long.

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2 years ago