Question

surface area of cylinders
independent practice
name avareeg
date 1/12/26 pd 8b
8th 75 (8.7b) due tmw
after class, mrs. sandoval picked up several pieces of paper containing students’ work from
the day.
ella
2πrh + 2πr²
2π(8)(4) + 2π(8²)
603.19 units²
shawn
2πrh
2π(8)(5)
251.33 units²
levi
2πrh + 2πr²
2π(2)(5) + 2π(2²)
87.96 units²
lorenzo
2πrh + 2πr²
2π(8)(5) + 2π(8²)
653.45 units²
ruby
2πrh + 2πr²
2π(4)(8) + 2π(4²)
301.59 units²
katrina
2πrh
2π(2)(5)
62.83 units²
use the students’ work to answer questions 1-7.

1. which student found the

total surface area of a
cylinder with a radius of 8
units and a height of 5 units?

1. which student found the

total surface area of a
cylinder with a height that was
two times greater than its
radius?
ruby

1. which student found the

total surface area of a
cylinder that had a diameter
of 4 units?

1. which students found the lateral surface

area of a cylinder?
s=2πrh+2πr²

1. draw a sketch of the cylinder that ella was

working on. label the radius and the height of
the cylinder.

1. find the lateral surface area of lorenzo’s

cylinder.

1. find the total surface area of katrina’s

cylinder.

Explanation:

Step1: Identify total surface area formula

Total surface area of a cylinder: $SA = 2\pi rh + 2\pi r^2$
Lateral surface area of a cylinder: $LA = 2\pi rh$

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Question 1

Step1: Match r=8, h=5 to work

Look for $2\pi(8)(5) + 2\pi(8^2)$

Step2: Identify matching student

Lorenzo's work matches this calculation.

---

Question 2

Step1: Define h=2r condition

If $h=2r$, total surface area is $2\pi r(2r) + 2\pi r^2 = 4\pi r^2 + 2\pi r^2 = 6\pi r^2$

Step2: Match to student work

Ruby's work: $2\pi(4)(8) + 2\pi(4^2)$; here $h=8=2*4=2r$, which fits.

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Question 3

Step1: Calculate radius from diameter

Diameter=4, so $r=\frac{4}{2}=2$

Step2: Match r=2 to total SA work

Look for $2\pi(2)h + 2\pi(2^2)$; Levi's work matches this.

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Question 4

Step1: Identify lateral SA formula

Lateral surface area uses only $2\pi rh$

Step2: Find matching students

Shawn and Katrina used only $2\pi rh$.

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Question 5

Step1: Extract Ella's r and h

From Ella's work: $r=8$, $h=4$

Step2: Describe cylinder sketch

Draw a cylinder, label radius $r=8$ units on the circular base, label height $h=4$ units on the vertical side.

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Question 6

Step1: Extract Lorenzo's r and h

$r=8$, $h=5$

Step2: Calculate lateral surface area

$LA = 2\pi rh = 2\pi(8)(5) = 80\pi \approx 251.33$ units²

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Question 7

Step1: Extract Katrina's r and h

$r=2$, $h=5$

Step2: Calculate total surface area

$SA = 2\pi rh + 2\pi r^2 = 2\pi(2)(5) + 2\pi(2^2) = 20\pi + 8\pi = 28\pi \approx 87.96$ units²

Answer:

1. Lorenzo
2. Ruby
3. Levi
4. Shawn, Katrina
5. (Sketch: A cylinder with circular bases; label the radius of the base as 8 units, and the vertical height of the cylinder as 4 units.)
6. $251.33$ units²
7. $87.96$ units²