Surface Area & Volume • Topic 2 of 3

Surface Area and Volume of Cylinders

What is a Cylinder? A cylinder is a three-dimensional solid with two parallel circular bases connected by a curved surface. Examples: a soda can, a pipe, a candle.

Parts of a Cylinder:

Radius ($r$): distance from center to edge of circular base
Height ($h$): perpendicular distance between the two bases

Formulas for a Cylinder:

Measurement	Formula
Curved Surface Area (CSA)	$2\pi r h$
Total Surface Area (TSA)	$2\pi r h + 2\pi r^2 = 2\pi r (r + h)$
Volume	$\pi r^2 h$

Understanding the Formulas:

Curved surface area = circumference of base × height = $(2\pi r) \times h$
Volume = area of base × height = $(\pi r^2) \times h$

Comparison of Solids:

Solid	TSA Formula	Volume Formula
Cube	$6a^2$	$a^3$
Cuboid	$2(lb + bh + hl)$	$l \times b \times h$
Cylinder	$2\pi r(r + h)$	$\pi r^2 h$

Solved Examples

Worked Example

Find the curved surface area and total surface area of a cylinder with radius 7 cm and height 10 cm. (Use $\pi = \frac{22}{7}$)

Solution- CSA = $2\pi r h = 2 \times \frac{22}{7} \times 7 \times 10 = 2 \times 22 \times 10 = 440$ cm² - TSA = $2\pi r (r + h) = 2 \times \frac{22}{7} \times 7 \times (7 + 10)$ - $= 2 \times 22 \times 17 = 748$ cm² - **Answer:** CSA = 440 cm², TSA = 748 cm² *Example 2: Find the volume of a cylinder with radius 3.5 cm and height 12 cm. (Use $\pi = \frac{22}{7}$) Solution: - Volume = $\pi r^2 h = \frac{22}{7} \times (3.5)^2 \times 12$ - $(3.5)^2 = 12.25 = \frac{49}{4}$ - Volume = $\frac{22}{7} \times \frac{49}{4} \times 12 = 22 \times 7 \times 3 = 462$ cm³ - **Answer:** 462 cm³ *Example 3: A cylindrical water tank has a height of 10 m and a radius of 4 m. Find the cost of painting its curved surface at ₹50 per square meter. (Use $\pi = 3.14$) Solution: - CSA = $2\pi r h = 2 \times 3.14 \times 4 \times 10 = 2 \times 3.14 \times 40 = 251.2$ m² - Cost = $251.2 \times 50 = ₹12,560$ - **Answer:** ₹12,560

Key Points

Cylinder has two circular bases and one curved surface
Curved Surface Area (CSA) = $2\pi r h$
Total Surface Area (TSA) = $2\pi r (r + h)$
Volume = $\pi r^2 h$
CSA is the area of the curved surface only; TSA includes both circular ends
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Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The volume of a cylinder is:

Explanation: $\pi r^2 h$.

Q2.The curved surface area of a cylinder is:

Explanation: $2\pi r h$.

Q3.The total surface area of a cylinder is:

Explanation: $2\pi r(r+h)$.

Q4.A cylinder has how many circular faces?

Explanation: Top and bottom.

Practice more MCQs → 📝 Assignment · 35 marks

Measurement	Formula
Curved Surface Area (CSA)	\(2\pi r h\)
Total Surface Area (TSA)	\(2\pi r h + 2\pi r^2 = 2\pi r (r + h)\)
Volume	\(\pi r^2 h\)

Solid	TSA Formula	Volume Formula
Cube	\(6a^2\)	\(a^3\)
Cuboid	\(2(lb + bh + hl)\)	\(l \times b \times h\)
Cylinder	\(2\pi r(r + h)\)	\(\pi r^2 h\)