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3 years ago

A cone of radius 10 cm and height 16 cm is divided into two parts by a plane through the midpoint of its

Mathematics

1 answer:

bazaltina [42]3 years ago

7 0

Answer:

The ratio of their volumes (the top to bottom half) is 1/7

Step-by-step explanation:

The given parameters are;

The radius, r, of the cone = 10 cm

The height of the cone = 16 cm

The point at which the cone is divided = The midpoint of the its axis and parallel to its base

The ratio of the of the volume of the two parts is given as follows;

The volume, V of the entire cone = 1/3 × Base area (π·r²) × Height, h

Therefore;

V = 1/3 × π × 10² × 16 =1600·π/3 = 1675.52 cm³

The height at which the cone is divided = 16/2 = 8 cm

The height, h₁ of the uppermost divided cone = 8 cm

The ratio of the radius to the height of the cone = 10/16 = 5/8

The radius r₁, of the uppermost divided cone = The height of the uppermost divided cone × The ratio of the radius to the height of the cone

∴ r₁ = 8 × 5/8 = 5 cm

The volume, V₁, of the uppermost divided cone = 1/3 × (π·r₁²) × h₁

∴ V₁ = 1/3 × π × 5² × 8 = 200·π/3 = 209.44 cm³

Which gives;

The volume of the lower cone, V₂ = V - V₁

V₂ = 1675.52 cm³ - 209.44 cm³ = 1400·π/3 = 1466.1 cm³

The ratio of their volumes V₁ : V₂ = V₁/V₂ = (200·π/3)/(1400·π/3) = 209.44/1466.1 = 1/7.

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Given klmn is a trapezoid, kl = mn, m<1 = m<2, lm/kn = 8/9, pklmn = 132. Find: the length of the legs

Ilia_Sergeevich [38]

Answer:

The length of legs lm, mn, and lk is 32 while that of kn is 36.

Step-by-step explanation:

The diagram is attached in the answer.

As both the angles are equal thus the two forms isosceles triangles. This is true because the converse of base angle theorem is applicable here. The theorem clearly states that when a trapezoid is divided by the diagonal, it forms two set of angles where m<1=m<2 and m<lmk=m<nmk

This leads the two set of legs such as

$\dfrac{lm}{kn}=\dfrac{8}{9}$

Or this could be written as

$lm=8x\\kn=9x$

Now the remaining two sides are given as

$lk=lm$ as this form an isosceles triangle so

$lk=8x$

Similarly

$mn=lm\\$

$mn=8x$

Now the perimeter is given as

$\text{perimeter}=lm+mn+kn+lk\\$

Here perimeter is given as 132 so this gives:

$\text{perimeter}=lm+mn+kn+lk\\132=8x+8x+8x+9x\\132=33x\\x=\dfrac{132}{33}\\x=4$

So the four legs are of length as given below:

$lm=8x=8\times 4=32\\mn=8x=8\times 4=32\\lk=8x=8\times 4=32\\kn=9x=9\times4=36$

So the length of legs lm, mn, and lk is 32 while that of kn is 36.

6 0

2 years ago

Qasim and Alejandra both earn $15 an hour at their job. This week Alejandra worked three hours more than Qasim. If h represents

joja [24]

Answer:

Alejandra worked 8 hours and Qasim worked 5

Step-by-step explanation:

195/15 is 13. They worked 13 hours in total. 8 is 3 more than 5 and together they equal 13.

8 0

3 years ago

7. Five swimmers entered a competition. Four of the swimmers had their turns. Their scores are 9.8, 9.75, 9.79 and 9.81 seconds

arsen [322]

Answer:

We must order these decimals from least to greatest. Then we must determine how the least compares with the winning score.

9.80 -> 3

9.75 -> 1

9.79 -> 2

9.81 -> 4

The least decimal is 9.75. Now we must determine how 9.75 compare with the winning score.

The last swimmer must get a score less than 9.75 seconds in order to win.

5 0

2 years ago

Geometry math question no Guessing and Please show work thank you

ASHA 777 [7]

First we need to understand what is collinear and coplanar . Points that are on same plane are known as coplanar and points that are on same line are known as collinear .

Here , RLS are on the same plane but they are not on the same line . So the given three points are coplanar but not collinear .

Therefore the correct option is A.

8 0

3 years ago

1. x2 + 12x + 27 = 0<br> what’s the answer ?

Ostrovityanka [42]

Answer:

$x^{2}$ + 3x +9x +27 = 0

x(x+3)+9(x+3)=0

(x+3)(x+9)=0

x=-3, x=-9

Step-by-step explanation:

a=1 b=12 c=27

sum=12

factor=27x 1

3x9

also 3+9=12

8 0

3 years ago