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Area Calculation - Online Quiz
Following quiz provides Multiple Choice Questions (MCQs) related to Area Calculation. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.
Q 1 - A way of uniform width keeps running round within a rectangular Field 38m long and 32m wide. On the off chance that the way involves 600m2, then The width of the way is:
Answer : B
Explanation
area of the field = (32*38)m2= 1216m2 Let the width of the path be x mtr. Area without path= (38-2x) (32-2x) m2 = 1216+4x2-140x Area of the path= 1216- (1216+4x2-140x) = 140x-4x2 ∴ 140x-4x2=600 ⇒4x2-140x+600=0 ⇒x2-35x+150=0 ⇒ (x-30) (x-5) =0 ⇒x=5m
Q 2 - The biggest size of the bamboo can be set in a square of zone 100sq. meters is:
Answer : B
Explanation
side of the square = √100 m =10 m Largest size of the bamboo= length of the diagonal of the square. = √ (10) 2+ (10) 2m = √ 200m = 10√ 2m =(10*1.414) m 14.14m
Q 3 - The expense of covering a room 15m long with a rug 75cm wide at 90 p for every meter is Rs. 108. The broadness of the room is:
Answer : A
Explanation
Length of the carpet= (10800/90)m =120m Area of the room = Area of the carpet= (120*75/100) m2= 90m2 Breadth of the room = area/length = 90/15m =6m
Q 4 - The covering of a room twice the length it is board at the rate of 50 p for every square mtr. costs rs. 12.25 And the expense of painting its dividers the rate of 9 p for every square mtr. is rs. 6.30. The tallness of the room is:
Answer : A
Explanation
Let breadth = x mtr. Then, length = 2x mtr. Area of the floor = 1225/50 m2= 49/2 m2 ∴ X*2x= 49/2 ⇒x2 =49/4 ⇒x=7/2 ∴ L = 7m, b= 7/2 m Area of 4 walls = 630/9 m2 = 70 m2 2(7+ 7/2)* h= 70 ⇒ 2*21/2*h =70 ⇒h =70/21 m = 10/3m
Q 5 - The territory of the four dividers of the room is 168m2. The broadness and Length of the room is 8m and 6m. The length of the room is:
Answer : C
Explanation
2(L+8)*6= 168 ⇒L+8= 168/12= 14 ⇒L= (14-8) = 6m
Q 6 - Each side of an equilateral triangle measures 2√3cm.The length of its altitude is:
Answer : C
Explanation
Each side= 2√3 1/2 * base *altitude= √3/4* (2√3)2 = √3/4 *12 = 3√3 ⇒ 1/2 *2 √3* altitude= 3√3⇒altitude= 3cm
Q 7 - What is the proportion of the ranges of circles engraved and delineated in a square?
Answer : C
Explanation
Let, each side of the square be x. Then, its diagonal= √2x Radius of in circle = x/2 Radius of circumcircle= √2x/2 = x/ √2 Required ratio = π(x/2)2: π(x/√2)2 = πx2/4: πx2/2 = 2:4= 1:2
Q 8 - A circle is recorded in a square. An equilateral triangle of side
Answer : C
Explanation
Radius of circumcircle of the triangle = a/√ 3= 4√ 3/√ 3=4cm Side of the square = (2*4) =8cm Diagonal of the square = √ (8)2+ (8)2= √ 64+64 =√ 128 =√ 2*64 = 8√ 2 cm
Q 9 - If the side of a rhombus is 20cm and its shorter corner to corner is three-fourth of its more extended askew, then the range of the rhombus is:
Answer : C
Explanation
Let the longer diagonal be x cm , then shorter diagonal = (3/4)x cm ∴ AC= x cm and BD=(3/4 )x cm AO =1/2*AC =x/2 cm, BO= 1/2 BD= (3/8) X cm and AB= 20 cm In right ∆ AOB, we have AO2 +BO2 = AB2 (x/2) 2+ (3x/8) 2= (20) 2⇒x2/4+9x2/64=400 ⇒16x2+9x2=25600 ⇒25x2= 25600 ⇒x2=1024 ⇒ x=√1024= 32 cm ∴ AO =32/2=16cm, BO= (3/8*32) cm=12cm ∴ AC=2*AO= 32 cm, BD= 2*BO= 24cm Area of the rhombus = (1/2*32*24) cm2 =384 cm2
Q 10 - The range of a square field is 6050m2. The length of its corner to corner is
Answer : A
Explanation
Let the diagonal be d meter. Then, 1/2 d2=6050⇒ d2= 12100 ⇒d=√12100= 110 m.