Certificate IV in Tertiary Preparation: Measurement Activity Part B

This document presents the solutions to the Measurement Activity Part B assignment from a Certificate IV in Tertiary Preparation maths course. The assignment focuses on applying formulas to calculate the area and volume of various geometric shapes, including rectangles, semi-circles, prisms (square and triangular), cones, cuboids, triangular pyramids, cylinders, square base pyramids, and right rectangle pyramids. The solutions include detailed step-by-step calculations for each problem, demonstrating the application of relevant formulas and providing the final answers in appropriate units. The assignment requires students to calculate surface areas, perimeters, and volumes, reinforcing their understanding of measurement concepts. The solution is designed to aid students in understanding the problem-solving process and mastering the mathematical concepts involved.

PART B
Question 4
A.)
Length of pool l = 20 m
Width w = 7 m
Depth h = 1.2 m
Diameter of semicircle = 7
Radius of semicircle = 3.5 m
Area of semi-circle = πr2 / 2
= [ 3.14 * 3.5 * 3.5 ] /2
Area of semi-circle = 19.23 m2
Area of two semi-circles = 2 * 19.23 = 38.6 m2
Lenth of rectangle = 20 – [3.5+3.5] = 13 m
Width of rectangle = 7 m
Area of rectangle = 91 m2
Total surface area of pool = area of rectangle + area of 2 semi-circles
= 91 + 38.6
Total surface area of pool = 129.6 m2
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B.)
Volume of pool = Volume of rectangle + Volume of both semi-circles
Volume of rectangle = length * width * depth
= 13 * 7 * 1.2 = 109.2 m3
Volume of semi-circle = 0.5 * π r2 h
Radius r = 3.5 m
Height h= 1.2 m
Volume = 0.5 * 3.14 * 3.5 *3.5 * 1.2
= 23.07 m3
Volume of pool = 109.2 + 23.07
Volume of pool = 132.27 m3
Question 5
a.)
Square prism
Volume = a2h where a is base edge and h is height
Given h = 15.55 cm and a = 4 cm
Volume = 4 * 4* 15.55
Volume = 248.8 cm3
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b.)
Triangular prism
Volume = Base area * prism length
Given:
Prism length l = 12 cm
Dimension of base triangle: Base b = 5 cm
Height h = 4.5 cm
Base area = 0.5 * 5 * 4.5 = 11.25
Volume = 11.25 * 12
Volume = 135 cm3
c.)
Cone
3

Volume of cone = [1/3] *π r2 h
Given: diameter d = 15 cm
Radius r = 7.5 cm
Height h = 21 cm
Volume = [1/3] *3.14* 7.5 * 7.5 * 21
Volume = 1236.37 cm3
D.)
Cuboid
Length l = 15 cm
Width w = 7 cm
Height h =3 cm
Volume of cuboid = l * w * h = 15 * 7 *3
Volume = 315 cm3
E.)
4

Triangular pyramid
Volume = [1/3] * base area * height from base to apex
Height from base to apex = h1 = 10 cm
Base area = 0.5 * 7 * 8 = 28 cm
Volume = [1/3] * 28 * 10
Volume = 93.33 cm3
F.)
5

Cylinder
Volume = π r2 h
Diameter d = 8.55 cm
Radius r = 4.27 cm
Height h = 19 cm
Volume = 3.14 * 4.27 * 4.27 * 19
Volume =1087.77 cm3
G.)
Square base pyramid
Volume = [1/3] * Base area * height
Height = 22.50 cm
Length = 12 cm
Width = 9 cm
Base area = 12*9 = 108 cm2
Volume = [1/3] * 108 * 22.50
Volume = 810 cm3
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H.)
Triangular prism
Volume = Base area * prism length
Given:
Prism length l = 10 cm
Dimension of base triangle: Base b = 8 cm
Height h = 3 cm
Base area = 0.5 * 8 * 3 = 12
Volume = 12*10
Volume = 120 cm3
I.)
Right rectangle pyramid
Volume = [l*w*h] / 3
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Given l = 23.50 cm w = 22 cm h = 28 cm
Volume = [23.50* 22 * 28] / 3
Volume = 4825.33 cm3
J.)
Right angle triangular prism
Volume = Base area * prism length
Given:
Prism length l = 11 cm
Dimension of base triangle: Base b = 4 cm
Height h = 3 cm
Base area = 0.5 * 4* 3 = 6
Volume = 6*11
Volume = 66 cm3
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