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Maths Lead.

The document explores the surface area and volume calculations for prisms and cylinders, providing formulas and sample problems. It includes specific examples for a rectangular prism and a cylinder, detailing how to calculate their surface areas and volumes. Additionally, it presents practice problems for further understanding of the concepts.

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snbprockers
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68 views14 pages

Maths Lead.

The document explores the surface area and volume calculations for prisms and cylinders, providing formulas and sample problems. It includes specific examples for a rectangular prism and a cylinder, detailing how to calculate their surface areas and volumes. Additionally, it presents practice problems for further understanding of the concepts.

Uploaded by

snbprockers
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Surface Area

and Volume
Exploring the surface area and
volume of a prism and cylinder

BY DEETI MANANI
Lesson Done after UT 1
Ch 2 Making sense of algebra
Ch 6 Equations and rearranging formulae
Ch 7 Perimeter, area and volume Th
er
Ch 9 Sequences and sets e ar
e1
Ch 10 Straight lines and quadratic equations 0!
Ch 13 Understanding measurements
Ch 14 Further solving of equations and inequalities
Ch 17 Managing money
Ch 21 Ratio,rate and Proportion
Ch 22 More equations, formulae and functions
Todays mission: Chapter 7
Surface area of a prism and cylinder
Volume of a prism and cylinder
Sample problems
Surface Area of a Rectangular Prism
SA = 2 (lw + wh + hl)

h
w
l

Rectangular Prism The net consists of three


pairs of equal rectangles.
Surface Area
SA = 2 (lw + wh + hl)
l= 12 w=6 h=4
h = 4cm. SA = 2 [(12 × 6) + (6 × 4) + (4 × 12)]
SA = 2 (72 + 24 + 48)
w = 6cm. SA = 2 (144)
The surface area
l = 12cm.
SA = 288cm² is expressed in
square.
The surface area of the
rectangular prism is 288cm².
Volume V=l×w×h
V=l×w×h
l= 5 w=1 h=4
h = 4m V=5×1×4
V = 20m³
w = 1m
l = 5m
The volume is
expressed in cubic
The volume of the rectangular meter.
prism is 20 m³.
A Cylinder

r 2πr

h h

The net consists of a


rectangle and 2 congruent
circles.
Total Surface Area of a Cylinder
TSA = 2πr (h + r)
TSA = 2πr (h + r)
r= 4 h=6
2πr
TSA = 2πx4 (6 + 4)
TSA = 8π (10)
6cm TSA = 80π cm²
The surface area
TSA = 251 cm²
is expressed in
4cm square.

The surface area of the


cylinder is 251 cm² (3s.f).
Volume
3cm
v = π r² h
v = π r² h
r= 3 h=9
v = π x 3² x 9
9cm v=πx9x9
v = 81π
v = 254cm³
The volume is
The volume of the rectangular expressed in cubic
prism is 254cm³. centimeter.
Try This!
Sarah wants to decorate
her cereal box with colorful
wrapping paper.
h = 10 cm

How much wrapping paper


does she need to cover the
entire box?
w = 4 cm
l = 6 cm

Hint: SA = 2 (lw + wh + hl)


Answer Key
SA = 2 (lw + wh + hl)
SA = 2 [(6 x 4) + (4 x 10) + ( 10 x 6)]
SA = 2 (24 + 40 + 60)
h = 10 cm
SA = 2 (124)

SA = 248 cm².

w = 4 cm
l = 6 cm The surface area of the cereal box
is 248 cm².
Try This!
Mia is on her way to the gym,
she needs to fill her water
bottle.
h = 15 cm

The watter bottle has hight of


15cm and radius of 5cm.
calculate the volume of water
that can be filled in the bottle.

r = 5 cm
Hint: v = π r² h
divide the volume value by 1000
to get Liter
Answer Key
v = π r² h
v = π 5² x 15
v = 25π x 15
h = 15 cm v = 375π
v = 1178cm³.
v = 1.178 L.
The volume of the bottle
r = 5 cm
is 1.178 L.
Thank you
for your time

presentation by Deeti Manani

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