22582VIC Certificate IV Math: Perimeter, Area, Volume Calculations

This document presents solutions to a series of math problems focusing on calculating perimeter, area, and volume. The assignment covers a range of geometric shapes, including squares, rectangles, triangles, circles, and prisms. Solutions are provided for finding the perimeter of squares, rectangles, equilateral triangles, and composite shapes. Area calculations involve triangles, circles, rectangles, and squares, as well as composite figures. The volume section addresses prisms and cylinders, with detailed step-by-step calculations. The solutions demonstrate the application of relevant formulas and principles. The document also includes visual representations of shapes and their dimensions, enhancing the understanding of the problem-solving process. This homework assignment is designed to reinforce understanding of fundamental geometric concepts.

LEARNING ACTIVITY 25 - PERIMETER
1.
Perimeter of a square = 4* side
Therefore,
perimeter= 4*40 cm
= 160 cm
2.
Perimeter of a rectangle= 2 (length+ breadth)
Length= 60 cm
Breadth= 30 cm
Perimeter= 2 (60+30)
= 2* 90
= 180 cm
3.
Side= 35 cm
Perimeter of equilatral triangle = 3*side
= 3*35
= 105 cm
4.
Perimeter = sum of all four sides
= 20+30+25+24
= 99 cm
1

5.
Perimeter= sum of all 5 sides
=40+20+22+40+31
= 153 cm
6.
Circumference of a circle = π x diameter
d = 7.9 cm
circumference = π x 7.9
= 3.14* 7.9
= 24.806 cm
7.
Circumference of a circle = π x diameter
d = 6.3 cm
circumference = π * 6.3
= 3.14 * 6.3
= 19.782 cm
8.
Circumference of a circle= 2 π r
r = 7.3
circumference = 2 * π* r
= 2* 3.14* 7.3
= 45.844 cm
9.
2

Circumference of a circle= 2 π r
r = 7.6 cm
circumference = 2 * π* r
= 2* π* 7.6
= 47.728 cm
10.
Perimeter = perimeter of rectangle- 10 + sum of 2 sides of right triangle
= 2 (length+breadth) – 10 + sum of 2 sides of right triangle
= 2 (22+7) – 10 + (7.5 +12.5)
= 2 (29) – 10 + 20
= 58 – 10 + 20
= 68m
11.
Perimeter = perimeter of rectangle – diameter + ½ circumference
= 2 (length+breadth) – 4.1 + ½ π d
Where d= diameter
= 2 (11.1+5.1) – 4.1 + ½ πd
=2 (16.2) – 4.1 + 0.5 * 3.14 * 4.1
= 32.4 – 4.1 + 6.437
= 38.837- 4.1
= 34.737 km
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LEARNING ACTIVITY 26- AREA
1.
Area of triangle = ½ base * height
b= 10m
h= 11m
area= ½ * 10 * 11
= 5*11
= 55 m2
2.
Area of circle= π r2
r = 8 cm
area= 3.14 * 8 * 8
= 200.96 cm2
3.
Area of rectangle = length * breadth
Length= 9m
Breadth= 2m
Area= 2 * 9
= 18 cm2
4.
Area of square= side2
Side= 6m
Area= 6*6
4

= 36 m2
5.
Area= 7 * 3
= 21cm2
6.
Area= 3.14* 5 * 5
= 78.5 cm2
7.
Area= 3.14 * 12* 12
= 452.16 cm2
8.
Area= 9 * 9
= 81 mm2
9.
Area= ½ * 12 * 12
= 72 m2
10.
Area= area of rectangle + area of semicircle
= length * breadth + ½ π r2
= 16 * 11 + ½ * 3.14 * 5.5 * 5.5
= 176 + ½ * 94.985
= 176 + 47.5
= 223.5 m2
5

11.
Area= area of rectangle + area of triangle
= length * breadth + ½ * base * height
=17 * 12 + ½ * 12* 6
= 204 + 36
= 240 m2
12.
Area= area of rectangle + area of square
= length * breadth
= 11*4 + 5*5
= 44 + 25
= 69 cm2
13.
Area= area of triangle + area of semicircle
= ½ base * height + ½ π r2
= ½ * 9 * 6 + ½ * 3.14 * 4.5 * 4.5
= 27 + 31.8
= 57.8 cm2
LEARNING ACTIVITY 27- VOLUME
1.
Volume of prism = area of cross section * length
6

= 10*4*12
= 480 m3
2.
Volume= area of cross section * length
= π r2 * 14 cm
= 3.14 * 8 * 8 * 14
= 2813.44 cm3
3.
Volume of prism= area of cross section * length
= ½ base * height * 13mm
= ½ * 10* 10 * 13
= 650mm3
4.
Volume= 1/3* area of base * height
= 1/3 * (22*21) * 35
= 5390 m3
5.
Volume= 1/3 * area of base* height
= 1/3 * π r2h
= 1/3 * 3.14 * 2 * 2 * 12
= 4.19* 12
= 50.28 m3
6.
7

Volume= 1/3* area of base * height
= 1/3 * 32* 32* 50
= 1/3 * 1024 * 50
= 341.3 * 50
= 17065 ft3
Activity 28
Surface area of cylinder = 2πrh + 2πr2
Given:
Radius r = 8 cm
Height h = 8 cm
Surface area = 2 * π * 8 *8 + 2 * π * 8 *8
= 401.92 + 401.92
Surface area = 803.84
8

Given:
Radius r = 4 cm
Height h = 6 cm
Surface area = 2 * π * 4 * 6 + 2 * π * 4 *4
= 150.72 + 100.48
Surface area = 251.2
Area of front and back = 2 * 2 * 6 = 24 cm2
Area of top and bottom: 2* 2 * 8 = 32 cm2
Area of sides = 2 * 8 * 6 = 96 cm2
Total surface area of structure: 24 + 32 +96 = 152 cm2
Suface area = 152 cm2
9

Area of front and back = 2 * 18 * 5 = 180 cm2
Area of top and bottom: 2* 18 * 4 = 144 cm2
Area of sides = 2 * 4 * 5 = 40 cm2
Total surface area of structure: 180+ 144+ 40 = 364 cm2
Suface area = 364 cm2
Surface area of prism = bh + l* [s1 +s2 +s3]
10

B is bottom edge of triangle; h is height; l is prism length and s1; s2 and s3 are edges of base
triangle
On substituting values:
= 12 * [4+7+7] + 4*6
= 12 * 18 +24 = 240
Surface area = 240 cm2
Activity 29
1.) Square of side 2 m
Let 2 meter is denoted as 1-unit block. Thus the square with 2m side is drawn as:
2.) Rectangle with dimension 20 m x 50 m
Let 2 meter is denoted as 1-unit block. Thus the rectangle can be shown as:
11

3.) Rectangle with dimension 2 km x 5 km
Let 1 km represent 1-unit block:
12

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