MAP4C Lesson 4 Assignment: Calculating Area and Volume of Shapes

This document provides a comprehensive solution set for the MAP4C Lesson 4 assignment, which focuses on determining the area and volume of various geometric shapes. The assignment covers multiple-choice questions that require students to identify appropriate formulas, draw diagrams, and perform step-by-step calculations. The solutions include detailed diagrams, formula applications, and the correct answers for each question, covering concepts such as area of shaded regions, playing fields, surface area of prisms, and volume calculations. The assignment also touches on related concepts from previous lessons, such as trigonometric ratios, sine law and cosine law. The provided solutions aim to help students understand and master area and volume problems, offering clear explanations and correct answers for effective learning.

MAP4C Lesson 4 Assignment answers
Question 1
3units
5units
5units
2units
2units
1 box = 1 unit
Rectangle A = 5units × 3units
=15units2
Rectangle B = 5units × 2units
=10units2
Total area =15 + 10 = 25 units2
Choice “d”
Question 2
There exist two semi circles which add to one circle
Area= πr2= 22
7 ×19.52=1195.07 m2
Area of triangle = l ×w=39 m× 120 m=4680 m2
Total area =1195.07+4680=5875 m2
Question 3 Area of square
Area=a2=82=64 ∈¿2 ¿
Area of triangle
= 1
2 ×b × h= 1
2 × 15× 7=52.5 ¿2
Total area = 64 ¿2+52.5 ¿2=116.5 ¿2
There are ten pieces
¿( 116.5× 10)=1165¿2
But there are two coats
¿ ¿
8in
8in
7in
Choice “b”
Choice “d”

Question 4
A
B C
8.6ft
3.2ft
8.6ft
3.2ft
Area of triangle (A)
1
2 × a× b=1
2 × 8.62=36.98 ft2
Area of rectangle (B)
l ×w=3.2 ×8.6=27.52 ft2
Area of square
l2=3.2 ft2 =10.24 ft2
Total area =27.52+10.24+36.98
¿ 74.74 ft2
8.6ft
Question 5
9.6m6.7m
A
B C
Semicircle A
1
2 πr2=1
2 × 22
7 ×(6.7
2 )
2
=17.635 m2
Area of B and C
l ×w=16.3 ×9.6=156.48 m2
Total area = 17.635 cm2+156.48 cm2=174.115 m2
Choice “b”
Question 6
Area of the shaded part
Smaller square= l2=0.52=0.25 ¿2
Larger square= l2= (22) =4Area of the shaded region =
(4-0.25 )=3.75 ln2
Choice “c”
Choice “a”
Choice “b”

Question 7
Area of rectangle A
A=l× l=7 ×11=77 m2
Area of rectangle B
12 ×5=60 m2
Total area =77 ×60=137 m2
Cost=
$3.99=6m2
? =137m2
= $ 3.99 ×137
6 =$ 91.105
12m
B
A
Choice “b”
Question 8
Given volume= 900cm3
v=1
2 ×a × c × h= 1
2 ×11.5 ×19.5 × h=900
Height=8.1cm
Question 10
Volume of the prism is
1
2 × a× c × h= 1
2 × 4.3 ×6.4 × 3.8=52.288 ¿3
=52.29 ¿3
Choice “d”
Choice “d”

Question 10
Volume of square base prism
v=a2 h=2.62 × 7.1=47.996 ft3
=48 ft3
Choice “c”
Question 11
Volume of rectangular prism
V=5000000 cm3
¿ l× b ×h=98 ×75 × h=5000000 cm3
500000
7350 =68 cm=hieght
Choice “d”
Question 12
Volume=Area of ˚×hieght
π r2 h= 22
7 ×8.92 ×5.2=1294.5177 cm2
¿ 1294 cm2
Choice “a”

Question 13
A
B
Volume for A
V =l × b× h=26 ×94 × 94=229,736 cm3
Volume of B
V =l × b× h=26 ×136 ×94=332,384 cm3
Total volume= 229736+332384
=562,120cm3
= 562120
1000000 0.56212 m3 =0.56 m3
21cm
Choice “c”
Question 14
Volume of isosceles triangular prism
¿ 1
2 ×b × h ×l= 1
2 ×16.4 × 21.2× 17.5=3042 ¿3
¿ 3042 ¿3
Choice “a”

Question 15
Volume prism A, B, C
Volume=cross section ×height
Cross section=
( 12 ×12 ) + ( 12× 24 ) + ( 12 ×36 )=864 cm2
Volume=864 cm2 ×120 cm=103,680 cm3
A
B
C
A
Choice “c”