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CoCubes Areas Question and Answers Quiz-1

Question 1

Time: 00:00:00

If the sides of a triangle are 26 cm, 24 cm, and 10 cm, what is its area?

120 cm²

312 cm²

130 cm²

315 cm²

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Answer: Option A

Explanation:

First, we will be checking the nature of the triangle

By Pythagoras Theorem,

$\sqrt{24^{2}+10^{2}} = \sqrt{676}$

√676 = 26 cm

The triangle with sides 26 cm, 24 cm, and 10 cm is right-angled, where the hypotenuse is 26 cm.

Area of the triangle =

\frac{1}{2}\times 24\times 10

= 120 cm²

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Question 2

Time: 00:00:00

A chord AB of a circle of radius 5.25 cm makes an angle of 60° at the center of the circle. Find the area of the major segment.

84 cm²

84.02 cm²

84.12 cm²

84.10 cm²

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Solution:
Option(C) is correct

The chord AB makes an angle of 60 degrees at the center

AB and the radii at the end points make an equilateral triangle

Area of the minor sector

=60/360 × π × 5.25²

=14.4375 cm²

Area of the triangle

=√3/4 * 5.25²

= 34 × 5.25²

=11.93 cm²

Area of the minor segment = Area of the minor sector - Area of the triangle

=2.5 cm2=2.5 cm2

Area of the major segment = Area of the circle - Area of the minor segment

=86.62 cm²−2.5 cm²

84.12 cm²

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Question 3

Time: 00:00:00

What is the are of an equilateral triangle of side 16 cm?

48√3 cm²

9.6√3 cm²

64√3 cm²

9.6√3 cm²

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Answer: Option D

Explanation:

Area of an equilateral triangle = √3/4 S²

If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm²

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Question 4

Time: 00:00:00

Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?

480 sq.m

720 sq.m

225 sq.m

360 sq.m

None of these

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Capture

since diagonals bisect at right angles in a rhombus.

BE² + AE² = AB²

25² = 15² + AE² AE = √(625 - 225) = √400 = 20,

AC = 20 + 20 = 40 cm.

Area of a rhombus = 1/2 * d₁d₂

= 1/2 * 40 * 30 = 600 sq.cm.

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Question 5

Time: 00:00:00

The ratio of the volumes of two cubes is 729: 1331. What is the ratio of their total surface areas?

81 : 121

729 : 1331

9 : 11

27 : 121

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Answer: Option A

Explanation:

Ratio of the sides = ³√729 : ³√1331 = 9 : 11

Ratio of surface areas = 9² : 11² = 81 : 121

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Question 6

Time: 00:00:00

An order was placed for the supply of a carpet whose length and breadth were in the ratio of 3: 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but there was no change in its parameter. Find the ratio of the areas of the carpets in both cases.

4 : 3

4 : 1

8 : 7

6 : 5

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Answer: Option B

Explanation:

Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.

Let the dimensions of the carpet in the second case be 7y, 3y units respectively.

From the data,.

2(3x + 2x) = 2(7y + 3y)

=> 5x = 10y

=> x = 2y

Required ratio of the areas of the carpet in both the cases

= 3x * 2x : 7y : 3y

= 6x² : 21y²

= 6 * (2y)² : 21y²

= 6 * 4y² : 21y²

= 8 : 7

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Question 7

Time: 00:00:00

What will be the cost of building a fence around a square plot with an area equal to 289 sq ft, if the price per foot of building the fence is Rs 58?

Rs. 3828

Rs. 4176

Rs. 3944

Cannot be determined

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Answer: Option A

Explanation:

Let the side of the square plot be a ft.

a² = 289 => a = 17

Length of the fence = Perimeter of the plot = 4a = 68 ft.

Cost of building the fence = 68 x 58 = Rs. 3944.

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Question 8

Time: 00:00:00

The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?

400 cm

800 cm

600 cm

1000 cm

None of these

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Explanation:

Area of the square = s * s = 5(125 * 64)

=> s = 25 * 8 = 200 cm

Perimeter of the square = 4 * 200 = 800 cm.

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Question 9

Time: 00:00:00

The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.

18 : 5

7 : 16

5 : 14

5 : 32

None of these.

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Answer: Option E

Explanation:

Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a² = 4096 = 2¹²
a = (2¹²)^1/2 = 2⁶ = 64
L = 2a and b = a - 24
b : l = a - 24 : 2a = 40 : 128 = 5 : 16

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Question 10

Time: 00:00:00

The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?

21 m

18 m

27 m

20 m

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Explanation:

Let the length and the breadth of the floor be l m and b m respectively.

l = b + 200% of b = b + 2b = 3b

Area of the floor = 324/3 = 108 sq m

l x b = 108 i.e., l x (l/3) = 108

l² = 324 => l = 18.

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