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18.07.2022

A cylinder has a height of 16 inches and a diameter of 34 inches. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.

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09.07.2023, solved by verified expert

Rajat Thapa

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Mathematics, DAV Post Graduate College

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Ⲁⲛ⳽ⲱⲉⲅ:Volume = 14,519.36 inch³Ⲋⲟⳑⳙⲧⳕⲟⲛ :

We are given that:

Height of cylinder = 16 inches Diameter of cylinder = 34 inches We have to use π = 3.14

Ⳙ⳽ⲓⲛⳋ ⳨ⲟⲅⲙⳙⳑɑ:

Since, cylinder has circular ends , it's volume is given by the formula:

Ⲧⲏⲉⲅⲉ⳨ⲟⲅⲉ:

‎ㅤ‎ㅤ‎ ‎ㅤ‎ㅤ‎~Hence, the volume of given cylinder is 14,519.36 cube inches.

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Mathematics

A cylinder has a height of 16 inches and a diameter of 34 inches. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.

Step-by-step answer

P Answered by Specialist

Ⲁⲛ⳽ⲱⲉⲅ:Volume = 14,519.36 inch³Ⲋⲟⳑⳙⲧⳕⲟⲛ :

We are given that:

Height of cylinder = 16 inches Diameter of cylinder = 34 inches We have to use π = 3.14

Ⳙ⳽ⲓⲛⳋ ⳨ⲟⲅⲙⳙⳑɑ:

Since, cylinder has circular ends , it's volume is given by the formula:

$\quad\hookrightarrow\quad {\pmb{\sf { \pi r^2 h }} }$

Ⲧⲏⲉⲅⲉ⳨ⲟⲅⲉ:

$\quad :\implies\quad \sf {V = \pi r^2 h }$

$\quad :\implies \quad \sf { V =\pi\left( \cancel{\dfrac{34}{2}}\right)^2\times 16}$

$\quad :\implies\quad \sf {V = 3.14 \times (17)^2 \times 16 }$

$\quad :\implies\quad \sf { V = 3.14\times 289 \times 16}$

$\quad :\implies \quad{\pmb{ \sf {V = 14,519.36}} }$

‎ㅤ‎ㅤ‎ ‎ㅤ‎ㅤ‎~Hence, the volume of given cylinder is 14,519.36 cube inches.

Mathematics

Factorise -75ab² - 15ac 5a(3b - c) -15b²(3a + c) -15a(5b² + c) 15a(5b² - c) A triangle has a base of length 6 cm and an area of less than 12 cm². Which of the following gives the height h of the triangle h 4 cm h 6cm h 12 cm h 24 cm Expand (2x-3)(2x +3) 4x² + 12x + 9 4x² - 12x – 9 4x² - 9 4x² + 9 A woman buys 8 tubers of yam at #200 each and sells them at a profit of 12%. Calculate the selling price. #192 #1600 #1792 #2000 What is the size of each angle of a regular 15-sided polygon? 78⁰ 156⁰ 185⁰ 200⁰ The height of a boy is t cm. His father is

Step-by-step answer

P Answered by PhD

1) -15·a·(5·b² + c)

2) h < 4

3) 4·x² - 9

4) 1792

5) 156°

6) 2t cm

7) 2·a·m·(2·m - 3)

8) 10 cm

9) 0.00051

10) #47,250

11) -10·p·q

12) 1.35 × 10⁻⁴

13) 320°

14) 20 cm

15) 12·x²·y²

16) 6.36 × 10⁵

17) 4 cm

18) 225°

19) 1034 cm²

20) 29

Step-by-step explanation:

1) The given expression is -75·a·b - 15·a·c

Which can be expressed as -15·a·(5·b² + c)

2) The height, h < 2 × 12/6 = 4

h < 4

3) (2·x - 3)·(2·x + 3) = 4·x² - 9

4) The selling price = 1.12 × 200 × 8 = 1792

5) The interior angle of a polygon is given by the relation;

(n - 2)×180/n for 15, we get;

(15 - 2)×180/15 = 156°

6) 2t cm

7) 4·a·m² - 6·a·m = 2·a·m·(2·m - 3)

8) Slant height = √(8² + 6²) = 10 cm

9) 51 × 10⁻⁵ = 0.00051

10) Cash price = #54,000 × (1 - 0.125) = #47,250

11) -40·p·q÷(-2)² = -10·p·q

12) 0.003 × 0.045 = 1.35 × 10⁻⁴

13) N40°W = 320°

14) The base diameter of the cylinder = √(4 × (700×π cm³/7)/π) = 20 cm

15) The LCM of 2·x²·y, 3·x·y² is 12·x²·y²

16) 636,000 = 6.36 × 10⁵

17) 1/3·π·r²·h₁ = π·r²·h₂

h₂/h₁ = 1/3·π·r²/( π·r²) = 1/3

h₂/12 = 1/3

h₂ = 12/3 = 4 cm, the height of the cylinder = 4 cm

18) The angle = 180 + 45 = 225°

19) The total surface area = 22/7×14²/4 + 22/7 ×14 × 20 = 1034 cm²

20) The number is 58/2 = 29.

Chemistry

Heptane and water do not mix, and heptane has a lower density (0.684 g/mL) than water (1.00 g/mL). A 100-mL graduated cylinder with an inside diameter of 3.16 cm contains 34.6 g of heptane and 34.0 g of water. What is the combined height of the two liquid layers in the cylinder? The volume of a cylinder is π r2h, where r is the radius and h is the height.

Step-by-step answer

P Answered by Specialist

h=100.8cm

Explanation:

Hello,

In this case, considering the density and mass of both water and heptane we first compute the volume of each one:

$V_{water}=\frac{m_{water}}{\rho _{water}}=\frac{34g}{1.00g/mL}=34mL\\ \\V_{heptane}=\frac{m_{heptane}}{\rho _{heptane}}=\frac{34.6g}{0.684g/mL}=50.6mL\\$

Now, the total volume is:

V=50.6mL+34mL=84.6mL

Which is equal to:

V=84.6cm^3

Then, by knowing that the volume of a cylinder is πr²h or π(D/2)²h, we solve for the height as follows:

$h=\frac{V}{\pi (D/2)^2} \\\\h=\frac{84.6cm^3}{\pi (3.16cm/2)^2} \\\\h=100.8cm$

Best regards.

Mathematics

Acd tower is shaped like a cylinder and holds cds with a diameter of 4.75 inches. if the cd tower is 12 inches tall, what is its volume in cubic inches? use 3.14 for pi. round your answer to the nearest hundredth. a. 212.54 cubic inches b. 231.56 cubic inches c. 850.16 cubic inches d. 867.34 cubic inches

Step-by-step answer

P Answered by PhD

Cylinder Volume = π • r² • height
Cylinder Volume = 3.14 * 2.375^2 * 12
Cylinder Volume = 3.14 * 5.640625 * 12
Cylinder Volume = 212.53875
Cylinder Volume = 212.54 (rounded)
answer is A

Mathematics

50 points for the : ) question 3 calculate the lateral area of a cube with side measurement of 4.1 ft. 64 cu. ft. 16 sq. ft. 67.24 sq. ft. 66 cu. ft. 2 points question 4 find the surface area of a cylinder with a diameter of 62 cm. and a height of 85 cm. 22582.88 sq. cm. 23045 sq. cm. 22582.88 cu. ft. 19565.34 sq. cm. 2 points question 6 find the surface area of a pyramid with a square base with sides measuring 5 cm. and whose slant height is 9 cm. 115 sq. cm. 110 sq. cm. 22.5 sq. cm. 90 sq. cm. 2 points question 10 find the lateral area of a rectangular

Step-by-step answer

P Answered by PhD

Q3. 67.24 sq. ft.Q4. 22582.88 sq. cm.Q6. 115 sq. cm.Q10. 240 sq. in.

Step-by-step explanation:

Q3.

The formula of a lateral area of a cube with side s:

LA=4s^2

We have s = 4.1 ft.

Substitute:

$LA=4(4.1^2)=4(16.81)=67.24\ ft^2$

Q4.

The formula of a surface area if a cylinder:

$SA=2\pi r^2+2\pi rH$

r - radius

H - height

We have 2r = 62 cm → r = 31 cm, H = 85 cm.

Substitute:

$SA=2\pi(31^2)+2\pi(31)(85)=2\pi(961)+5270\pi=1922\pi+5270\pi=7192\pi\ cm^2$

$\pi\approx3.14\to SA\approx(7192)(3.14)=22582.88\ cm^2$

Q6.

The surface area of a square piramid is

base - square

lateral sides - four triangles

The formula of an area of a square with sides s:

A=s^2

The formula of an area of a triangle with base b and height h:

$A=\dfrac{bh}{2}$

We have s = 5 cm, b = s = 5 cm, h = 9 cm.

Substitute:

$A_{\square}=5^2=25\ cm^2\\\\A_{\triangle}=\dfrac{(5)(9)}{2}=\dfrac{45}{2}=22.5\ cm^2$

The surface area:

$SA=A_{\square}+4A_{\triangle}\\\\SA=25+4(22.5)=25+90=115\ cm^2$

Q10.

The lateral sides are two pairs of rectangles.

The formula of an area of a rectangle:

$A=l\cdot w$

l - length

w - width

We have the rectangles:

5 in × 10 in and 7 in × 10 in

Substitute:

$A_1=(5)(10)=50\ in^2\\\\A_2=(7)(10)=70\ in^2$

The lateral area:

$LA=2A_1+2A_2\\\\LA=2(50)+2(70)=100+140=240\ in^2$

Mathematics

Acd tower is shaped like a cylinder and holds cds with a diameter of 4.75 inches. if the cd tower is 12 inches tall, what is the volume, in cubic inches, that it can hold? use 3.14 for pi. round your answer to the nearest hundredth. 212.54 in3 231.56 in3 850.16 in3 867.34 in3

Step-by-step answer

P Answered by PhD

Vcyl=hpr^2, r=2.375, p=3.24, h=12

V=12(3.14)2.375^2=212.54 in^3

Mathematics

Step-by-step answer

P Answered by PhD

Cylinder Volume = π • r² • height
Cylinder Volume = 3.14 * 2.375^2 * 12
Cylinder Volume = 3.14 * 5.640625 * 12
Cylinder Volume = 212.53875
Cylinder Volume = 212.54 (rounded)
answer is A

Mathematics

Step-by-step answer

P Answered by PhD

Q3. 67.24 sq. ft.Q4. 22582.88 sq. cm.Q6. 115 sq. cm.Q10. 240 sq. in.

Step-by-step explanation:

Q3.

The formula of a lateral area of a cube with side s:

LA=4s^2

We have s = 4.1 ft.

Substitute:

$LA=4(4.1^2)=4(16.81)=67.24\ ft^2$

Q4.

The formula of a surface area if a cylinder:

$SA=2\pi r^2+2\pi rH$

r - radius

H - height

We have 2r = 62 cm → r = 31 cm, H = 85 cm.

Substitute:

$SA=2\pi(31^2)+2\pi(31)(85)=2\pi(961)+5270\pi=1922\pi+5270\pi=7192\pi\ cm^2$

$\pi\approx3.14\to SA\approx(7192)(3.14)=22582.88\ cm^2$

Q6.

The surface area of a square piramid is

base - square

lateral sides - four triangles

The formula of an area of a square with sides s:

A=s^2

The formula of an area of a triangle with base b and height h:

$A=\dfrac{bh}{2}$

We have s = 5 cm, b = s = 5 cm, h = 9 cm.

Substitute:

$A_{\square}=5^2=25\ cm^2\\\\A_{\triangle}=\dfrac{(5)(9)}{2}=\dfrac{45}{2}=22.5\ cm^2$

The surface area:

$SA=A_{\square}+4A_{\triangle}\\\\SA=25+4(22.5)=25+90=115\ cm^2$

Q10.

The lateral sides are two pairs of rectangles.

The formula of an area of a rectangle:

$A=l\cdot w$

l - length

w - width

We have the rectangles:

5 in × 10 in and 7 in × 10 in

Substitute:

$A_1=(5)(10)=50\ in^2\\\\A_2=(7)(10)=70\ in^2$

The lateral area:

$LA=2A_1+2A_2\\\\LA=2(50)+2(70)=100+140=240\ in^2$

Mathematics

Step-by-step answer

P Answered by PhD

212.54 in3

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Volume of a cylinder: π r² h

Where:

r = radius (also r= diameter /2) h= height

Replacing with the values given:

r = 4.75/2 = 2.375 in

h = 12in

V = π r² h

V= π (2.375)² (12) = 3.14 (5.640625) 12 =212.54 in3

So, the correct option is 212.54in3

Feel free to ask for more if needed or if you did not understand something.

Mathematics

The diameter of a specific hydraulic cylinder shaft is 2.1634 inches the diameter of another shaft is 3.0187inches. what is the difference in the diameter

Step-by-step answer

P Answered by Master

We are given

The diameter of a specific hydraulic cylinder shaft is 2.1634 inches

so, d_1=2.1634

the diameter of another shaft is 3.0187inches

so, d_2=3.0187

now, we can find the difference

the difference in the diameter=(the diameter of another shaft)-(The diameter of a specific hydraulic cylinder shaft)

now, we can plug values

the difference in the diameter is

=d_2-d_1

we can plug values

=3.0187-2.1634

the difference in the diameter is 0.8553 inches..........Answer

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A cylinder has a height of 16 inches and a diameter of 34 inches. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.

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