Paulo's Surface Area of a Prism

Homewor
pg 54, question 2

2. Calculate the surface area of each rectangular prism to the nearest tenth of a centimetre squared.








Front:
5x11.5=57.5cm2
5x11.5=57.5cm2

Top:
11.5x3.2=36.8cm2
11.5x3.2=36.8cm2

Side:
5x3.2=16cm2
5x3.2=16cm2
---------------
TSA 220.6cm2

b)
Front:
12x10.4=124.8cm2
12x10.4=124.8cm2

Top:
10.4x4.5=46.8cm2
10.4x4.5=46.8cm2

Side:
5x3.2=16cm2
5x3.2=16cm2
----------------
TSA 375.2 cm2

pg 54, question 3

3

a)
triangle+ 7x8/2= 28cm2
triangle+ 7x8/2=28cm2

a=2.5x8=20cm2
a=2.5x7=17.5cm2
a=2.5x=10.6=26.5cm2
------------------------
TSA 120cm2

pg 53, question 4




3.14x4.1x4.1)x11

Math Test Questions 1 and 3

Answers for questions 1 and 3 on the test

1

3

Here is a website for practice

http://www.thatquiz.org/tq-4/?-j2080-la

Cylinder Volume and Volume Problems

Jumbo

V= π.r.r.h

V= 3.14.10.10.40

V= 12 560cm³

Popcorn Lover's

V= π.r.r.h

V= 3.14.15.15.20

V= 14 130cm³

I think that Martha should get the Popcorn Lover's one because it has more volume to get more popcorn.

Inside:

V= π.r.r.h

V= 3.14 .0.4 .0.4 .10

V= 5.024cm³

Outside:

V= π.r.r.h

V= 3.14. 0.5 . 0.5 . 10

V= 7.85cm³

7.85 - 5.024=2.826m³

Surface Area- cylinders.

Cylinders:
The bases of the cylinder are circles.

Circumference:
-The perimeter of a circle .


Diameter:
- Halfs the circle.

Radius:
- Half of the diatmeter


*Formulas :
Finding the circumference:
πd= c
Finding the diamer :
2r=d or c/π= d
Finding the radius :
d/2= r

*Area of circle:
π x r 2
(3.14 x radius squared)


* Homework questions :)





A= πr²
A = 314 x 3.2 <sup>2
A= 3.14 x 10.24
A= 232.15 cm 2

A=</sup>π <sup>r2
A= 3.14 x 62
A= 3.14 x 36
A=113.04cm 2

d/2= r
25/2 = r
25/2= 12.5
A=</sup> π<sup>r2
A=3.14 x 62
A= 3.14 x 36
A= 490.526 cm 2

A=</sup>π<sup>r2
A= 3.14 x 16.5 2
A- 3.14 x 272.25
A= 854.865 cm 2

c/ =d
18.84/ 3.14=d
18.84/ 3.14= 6
d/2= r
6/2= r
6/2= 3
A=</sup> π<sup>r2
A= 3.14x 32
A= 3.14 x 9
A= 28.26 cm2

c/ = d
31.4/ 3.14= d
31.4/3.14= 10
d/2 = r
10/2= r
10/2 = 5
A=</sup> π<sup>r2
A= 3.14 x 52
A= 3.14 x 25
A = 78.5 cm2

d/2 = r
15/2 = r
15/2= 7.5
A=</sup> π^{r2
A= 3.14 x 7.52}
A= 3.14 x 56.25
A= 176.63 cm2



Cylinder Volume and Volume Problems





a) d/2= r
10/2= 5cm^2

v= (πr^2) * h
v= (3.14 x 5 x 5 ) x 20
V= (78.5) x 20
V= 1570cm^3

b) d/2= r
1/2= o.5m^2

v= (πr^2) x h
v= (3.14 x 0.5 x o.5) x 1
v= (0.785) x 1
v= o.785m^3

c) d/2= r
18/2= 9cm^2

v= (πr^2) x h
v= (3.14 x 9 x 9) x 7.5
v= 254.34 x 7.5
v= 1907.55cm^3

Richard's Test Scribe

Rectangular Prism

lxw

Top - 6cm, 5cm 6x5 = 30cm2
6x5 = 30cm2

Front - 20cm, 6cm
20x6 = 120cm2
20x6 = 120cm2

Side - 20cm, 5cm
20x5 = 100cm2
20x5 = 100cm2
-------------------
TSA = 500cm2

Cylinder

d÷2 = r

8÷2 = r

8÷2 = 4cm2

(2 x 3.14 x 4 x 4) + (2 x r x 3.14 x 15)

100.48cm2 + 376.8cm2

= 477.28cm2

Cylinder Math Notes

When we think of cylinders we need to better understand circles.

Circle Terms

Radius- half of the diameter

Diameter- Cuts the circle in half

Circumference- The perimeter of the circle

Pi- The ratio between circumference:diameter or 3.14

Formulas

Circumference- pi x diameter = circumference

Radius- diameter/2 = radius

Diameter- 2 x radius = d or circumference/ pi = diameter

Area of a Circle

To find the area of a circle you use the equation:

pi x r2

It means multiply pi by the radius squared

Homework

Our homework is to find the area, diameter, circumference and radius of these circles.

I'll do the circles in order from left to right
a) d = c/pi r = d/2 a = pi x r2
d = 18.89/3.14 r = 6/2 a = 3.14 x 3 x 3
d = 6cm r = 3cm a = 28.26cm2

b) d = c/pi r = d/2 a = pi x r2
d = 31.4/3.14 r = 10/2 a = 3.14 x 5 x 5
d = 10cm r = 5cm a = 78.5 cm2

c) d = r x 2 c = pi x d a = pi x r2
d = 3.2 x 2 c = 3.14 x 6.4 a = 3.14 x 3.2 x3.2
d = 6.4cm c = 20.1cm a = 32.15cm2

d) d = r x 2 c = pi x d a = pi x r2
d = 6 x 2 c = 3.14 x 12 a = 3.14 x 6 x6
d = 12cm c = 37.68cm a = 113.04cm2

e) d = r x 2 c = pi x d a = pi x r2
d = 16.5 x 2 c = 3.14 x 33 a = 3.14 x 16.5 x 16.5
d = 33cm c = 103.62cm a = 854.87cm2

f) r = d/2 c = pi x d a = pi x r2
r = 25/2 c = 3.14 x 25 a = 3.14 x 12.5 x 12.5
r = 12.5cm c = 78.5cm a = 490.63cm2

g) r = d/2 c = pi x d a = pi x r2
r = 15/2 c = 3.14 x 15 a = 3.14 x 7.5 x 7.5
r = 7.5cm c = 47.1cm a = 176.63cm2

I had problems organizing the equations for the homework. If anyone has a suggestion to organize the homework please do comment. :)
I hope everyone now knows how to find the different parts of a circle.

Cylinder Volume and Volume Problems

Here is a problem from 7.3 to better understand calculating the volume of a cylinder.


To solve this cylinder problem we will need the formula: π x r x r x h
But we dont have the radius. We have the diameter. We will need the formula to find the radius: d/2 = r. In this question d= 20.3cm
20.3/2 = 10.15cm
Now we can do the formula
π x r x r x h = v
3.14 x 10.15 x 10.15 x 10 = 3234.9065cm^3

Here is a question from 7.4.


For this one we have to subtract the small cylinder from the big cylinder.
Big circle
pi x r x r x h = v
3.14 x 0.5 x 0.5 x 10 = v
7.85m^3 = v

Small circle
pi x r x r x h = v
3.14 x 0.4 x 0.4 x 10 = v
5.024m^3 = v

7.85 - 5.024 = 2.826m^3
Rounded it is 2.8m^3.

Cathlene's Surface Area Post

Question 2

(base x height ÷ 2 = area)

TSA= 342 cm ²

Question 4

(lenght x width = area)

TSA= 228 cm ²

Jayvee's Surface Area Scribe Post

2. A right rectangular prism has six faces. Why might you have to find the area of only three of the faces to be able to find the surface area? Use pictures and words to explain your thinking.

You only need to find the surface area of 3 faces because the top and bottom are the same, as well as the front and back, and the 2 sides.
.

4. Find the surface area of this CD case.
Front:
14x12.3 = 172.2cm2
14x12.3 = 172.2cm2

Top :
12.3x1 = 12.3cm2
12.3x1 = 12.3cm2

Side :
14x1 = 14cm2
14x1 = 14cm2

TSA = 397cm2

6. Cheese is sometimes packaged in a triangular box. How much cardboard would you need to cover this piece of cheese if you do not include overlapping? Calculate your answer to the nearest tenth of a square centimetre.


Front :
9.1x6.4 / 2 = 29.12cm2
9.1x6.4 / 2 = 29.12cm2

Top(Bottom) :
9.1x3 = 27.3cm2

Sides :
6.4x3 = 19.2cm2
6.4x3 = 19.2cm2

TSA = 123.94cm2

8. Paco builds a glass greenhouse.

A) How many glass faces does the greenhouse have?
The greenhouse have 5 faces.

B) How much glass does Paco need to buy?

Front :
1.8x1.1 / 2 = 0.99m2
1.8x1.1 / 2 = 0.99m2

Top (Bottom) :
2.4x1.8 = 4.32m2

Side :
2.4x1.1 = 2.64m2
2.4x1.1 = 2.64m2

TSA = 11.58m2

My Volume Question :



Question from 7.3
A) d/2 = r
2/2 = r
1 = r
v = PiexRxRxH
v = 3.14x1x1x0.6
v = 3.14x0.6
v = 1.884cm^3
B) 1.256/1(h) = 1.256
1.256 / 1(r) / 1(r) / 3.14 = 0.4m
C) First, find the volume if the water's depth is 0.7m
3.14 x 1(r) x 1(r) x 0.7 = 2.198m^2
Now, find the volume if the water's depth is 0.5m
3.14 x 1(r) x 1(r) x 0.7 = 1.5 = 1.57m^2
After you get both of the answers, subtract 1.57 from 2.198 = 0.62m^m3

Question from 7.4

First, find the volume of the bigger circle.
3.14 x 0.5 x 0.5 x 10 = 7.85m^2
Now, find the volume of the smaller circle.
3.14 x 0.4 x 0.4 x 10 = 5.024m^2
After you got both volumes, subtract 5.024 from 7.85
7.85 - 5.024 = 2.826m^3