Surface Area of Cylinder

MYP3 Mathematics

About Lesson

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Questions

Criterion A and C

QUESTION 1:

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Question 2:

Type 1: Find the Surface Area

Q1. Apply the formula for the total surface area to find the total surface area of a cylindrical water tank with a radius of 6 m and a height of 12 m.

Q2. Calculate the curved surface area of a metal pipe with a diameter of 10 cm and a height of 15 cm. Use π = 3.14.

Type 2: Find the Radius

Q3. Determine the base radius of a solid cylinder if its curved surface area is 314 m² and its height is 10 m.

Q4. Justify your answer by calculating the radius of a hollow cylindrical pipe if its outer curved surface area is 500 cm², the height is 25 cm, and π = 3.14.

Type 3: Find the Height

Q5. Calculate the height of a cylindrical container if its curved surface area is 660 cm² and its radius is 7 cm.

Q6. Determine the height of a cylindrical tower if its total surface area is 904 m² and its radius is 8 m.

Q7. Solve for the height of a hollow pipe if its outer curved surface area is 1200 cm², the outer radius is 10 cm, and π = 3.14.

Answers

Question 1:

a ≈ 352 cm²
b ≈ 341 cm²
c ≈ 44.9 cm²
d ≈ 100 m²
e ≈ 820 cm²
f ≈ 292 m²

Question 2 :

Q1: Total Surface Area of a Cylindrical Water Tank

Given:

Radius, $r=6r = 6$ m
Height, $h=12h = 12$ m

Formula for TSA:

$TSA=2πr(h+r)$

Substituting values:

$TSA=2\times3.14\times6\times(12+6)$

$2\times3.14\times6\times18$

$678.24$

Final Answer: 678.24 m²

Q2: Curved Surface Area of a Metal Pipe

Given:

Diameter = 10 cm → Radius = 5 cm
Height = 15 cm

Formula for CSA:

$CSA=2πrh$

$CSA=2\times3.14\times5\times15$

$471$

Final Answer: 471 cm²

Q3: Finding the Radius of a Solid Cylinder

Given:

CSA = 314 m²
Height, $h=10h = 10$ m

Formula:

$CSA=2πrh$

$r=CSA / 2πhr$

Substituting values:

$r=5$

Final Answer: 5 m

Q4: Finding the Radius of a Hollow Cylinder

Given:

Outer CSA = 500 cm²
Height, $h=25$

Formula:

$CSA=2πRh$

$R=CSA/2πh$

Substituting values:

$R=$ $3.18$

Final Answer: 3.18 cm

Q5: Finding the Height of a Cylindrical Container

Given:

CSA = 660 cm²
Radius, $r=7r = 7$ cm

Formula:

$CSA=2πrh$

Rearrange to find $hh$ :

$h=CSA/2πrh$

Substituting values:

$h=660 / 2\times3.14\times7$

$h=15 cm$

Final Answer: 15 cm

Q6: Finding the Height of a Cylindrical Tower

Given:

TSA = 904 m²
Radius, $r=8$

Formula:

$TSA=2πr(h+r)$

$h = 10m$

Final Answer: 10 m

Q7: Finding the Height of a Hollow Pipe

Given:

Outer CSA = 1200 cm²
Outer Radius, $R=10$

$CSA=2πRh$

$h=CSA / 2πR$

Substituting values:

$h$ $= 19.11 cm$

Final Answer: 19.11 cm