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3 years ago

The volume of a sphere is 904.32 cm3, find its radius and hence its curved surface area

Mathematics

1 answer:

Harlamova29_29 [7]3 years ago

5 0

Volume = $\frac{4}{3}$ * π * r³ = 904.32 cm³

radius = $\sqrt[3]{\frac{3*Volume}{4 * pi} }$ cm=

= $\sqrt[3]{\frac{3 * 904.32}{4 * 3.14} }$ cm=

= $\sqrt[3]{\frac{2712,96}{12.56} }$ cm=

= $\sqrt[3]{216}$ cm=

radius = 6 cm

surface = 4 * π * r² cm² =

= 4 * π * 6² cm² =

= 4 * 3.14 * 36 cm² =

= 452,16 cm²

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an initial investment of $9000 grows at an annual interest rate of 5% compounded continuously. how long will it take to double t

tino4ka555 [31]

Answer:

20 years

Step-by-step explanation:

9000/ 100= 900 = 10%

900/2= 450

450 x 2= 900

900 x 10= 9000

Now we multiply 10 by 2 because we doubled the value of our 450 into a 900 and now we get 20.

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3 years ago

Write a compound inequality to represent all of the numbers between -4 and 6.

OlgaM077 [116]

-4<x<6
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3 years ago

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2 years ago

Round to nearest thousandth!! (3 decimal places) photo attached

aliina [53]

Answer:

<em>Probability point lies on shaded region: ( About ) 0.294</em>

Step-by-step explanation:

<em>~ If we are to find the probability, we must find the area of the shaded figure, over that of the total area of this trapezoid ( whole figure ) ~</em>

Let us get the general dimensions. Firstly, the base of the trapezoid is composed of parts 5, 12, and 5. This is an isoceles trapezoid, meaning that the triangles ( shaded region ) are congruent to one another, including the altitudes. That would mean the non - shaded region is a parallelogram, provided altitudes are congruent and by definition of a trapezoid the bases are congruent.

1. Given the information above, the smaller base is congruent to the opposite side of the parallelogram created, so it is 12 units in length, the larger base being 12 + 5 + 5 ⇒ 22 units

2. By Pythagorean Theorem, if x ⇒ altitude of one of the triangles ( shaded region), 5^2 + x^2 = 13^2 ⇒ 25 + x^2 = 169 ⇒ x^2 = 144 ⇒ altitude = 12 units

3. Now we can find the area of this trapezoid by: ( base + base/2 ) * altitude ⇒ ( 12 + 22 / 2 ) * 12 ⇒ ( 34 / 2 ) * 12 ⇒ ( 17 ) * 12 ⇒ 204 units^2

5. The shaded region is composed of two triangles, and knowing the triangles are ≅, let us solve for the area of one triangle and multiply that by 2 to find the total area of the shaded region. Area of triangle: 1/2 * base * altitude ⇒ 1/2 * 5 * 12 ⇒ 30 units^2. Area of shaded region: 30 * 2 = 60 units^2

<em>Probability point lies on shaded region: 60/204 ⇒ ( About ) 0.294</em>

8 0

3 years ago

The incorrect work of a student to solve an equation 2(y + 6) = 4y is shown below.

Lina20 [59]

Answer:

<h3>⇒ A. 2 should be distributed as 2y + 12, y = 6</h3>

Step-by-step explanation:

Here are the steps to solve this equation:

<u>Given:</u>

First step: 2(y+6)-4y

Use the distributive property.

<u>Distributive property:</u>

2(y+6)

2*y=2y

2*6=12

2y+12

Isolate the term of y from one side of the equations.

2y+12=4y

Subtract by 12 from both sides.

2y+12-12=4y-12

Solve.

2y=4y-12

Then, you subtract by 4y from both sides.

2y-4y=4y-12-4y

Solve.

2y-4y=-2y

-2y=-12

Divide by -2 from both sides.

$\sf{\dfrac{-2y}{-2}=\dfrac{-12}{-2}}$

Solve.

Divide the numbers from left to right.

<u>Solutions:</u>

-12/-2=6

$\Longrightarrow: \boxed{\sf{y=6}}$

<u>Therefore, the correct answer is A. "2 should be distributed as 2y+12, y=6".</u>

I hope this helps. Let me know if you have any questions.

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2 years ago

The volume of a sphere is 904.32 cm3, find its radius and hence its curved surface area​

The volume of a sphere is 904.32 cm3, find its radius and hence its curved surface area