Mathematics, 22.05.2020 02:06 ulilliareinhart2

Geometry, plz help!

17. The volume of a sphere is 1548 pi meters cubed. What is the surface are of the sphere?

18. If the ratio of sides of two similar prisms is 2:3, what is the ratio of their volumes? (1pt)

19. The surface area of two similar solids is 121 yards squared and 361 yards squared. The volume of the larger solid is 1747 yards cubed. What is the volume of the smaller solid? (3pts)

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Answer from: alowery89

17. surface area ≈ 441.84

04π m² or 1387.38 m²

18. Ratio of volumes = 8/27

19. volume of the smaller solid = 339 yards³

Step-by-step explanation:

17 .

To find the surface area of the sphere we have to find the radius of the sphere first.

volume of a sphere = 4/3πr³

volume = 1548π m³

r = ?

volume of a sphere = 4/3πr³

1548π = 4/3 × π × r³

multiply both sides by 3/4

1548π × 3/4 = πr³

4644π/4 = πr³

1161π = πr³

divide both sides by π

r³ = 1161

cube root both sides

r = ∛1161

r = 10.5101942

r ≈ 10. 51

surface area of a sphere = 4πr²

surface area = 4 × π × 10.51²

surface area = 4 × 110.4601 × π

surface area = 441.8404π m²

surface area = 441.8404 × 3.14 = 1387.378856 m² ≈ 1387.38 m²

If two figure or solid are similar with scale factor or ratio of x/y then the ratio of their volume is (x/y)³. If the ratio of of two similar prism is 2 : 3 the volume will be (2/3)³ = 8/27 .

If two solids are similar then the ratio of their surface area is the squared of the scale factor.

121/361 = (x/y)²

square root both sides

x/y = 11/19

If two solids are similar then the ratio of their volume is the cube of the scale factor.

(11/19)³ = a/1747

1331/6859 = a/1747

cross multiply

6859a = 2325257

divide both sides by 6859

a = 2325257/6859

a = 339.008164455

a ≈ 339 yards³

volume of the smaller solid ≈ 339 yards³

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

Answer from: Quest

w'x is 0.

hope it

Me i need to pass so i can go on to the next thing plz someone me. will give

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17. The volume of a sphere is 1548 pi meters cubed. What is the surf...

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