TOP QUESTIONS AND ANSWERS FOR YOU

Maths

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8th

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February 28, 2022

3. A solid cube of side 12 cm is cut into 8 identical cubes. What will be the side of the new cube? Also, find the ratio between the surface area of the original cube and the total surface area of all the small cubes formed.

David Miller

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Student

Solution:

Maths

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8th

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February 28, 2022

2. The diameter of a garden roller is 1.4 m and it 2 m long. Find the maximum area covered by it 50

David Miller

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Student

Solution:

Maths

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8th

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February 28, 2022

1. In a building, there are 24 cylindrical pillars. For each pillar, radius is 28 m and height is 4 m. Find the total cost of painting the curved surface area of the pillars at the rate of ₹ 8 per m2.

David Miller

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Student

Solution:

Maths

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8th

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February 24, 2022

4. **Write 3.61492 x 106 in usual form.**

David Miller

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Student

Solution: 3.61492 x 106

= 3.61492 x 1000000

= 3614920

Maths

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8th

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February 24, 2022

3. **Express 0.00000000837 in standard form.**

David Miller

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Student

Maths

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8th

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February 24, 2022

2. ** Simplify [25 x t-4]/[5-3 x 10 x t-8]**

David Miller

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Student

Solution:

We can write the given expression as;

[52x t-4]/[5-3 x 5 x 2 x t-8]

= [52 x t-4+8]/[5-3+1 x2]

= [52+2 x t4]/[2]

= [54 x t4]/[2]

= [625/2] t4

Maths

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8th

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February 24, 2022

**1.If a new-born bear weighs 4 kg, calculate how many kilograms a five-year-old bear weigh if its weight increases by the power of 2 in 5 years?**

David Miller

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Student

Maths

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9th

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February 24, 2022

5. **In Fig. 6.40, ∠X = 62°, ∠XYZ = 54°. If YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of Δ XYZ, find ∠OZY and ∠YOZ.**

Joslin Smith

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Student

As we know, the sum of the interior angles of the triangle is 180°.

So, ?X +?XYZ + ?XZY = 180°

substituting the values as given in the question we get,

62° + 54° + ?XZY = 180°

Or, ?XZY = 64°

Now, As we know, ZO is the bisector so,

?OZY = ½ ?XZY

? ?OZY = 32°

Similarly, YO is a bisector and so,

?OYZ = ½ ?XYZ

Or, ?OYZ = 27° (As ?XYZ = 54°)

Now, as the sum of the interior angles of the triangle,

?OZY +?OYZ + ?O = 180°

Substituting their respective values we get,

?O = 180° – 32° – 27°

Or, ?O = 121°

Maths

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9th

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February 24, 2022

4. **In the Figure, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.**

Joslin Smith

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Student

Solution:

First, construct a line XY parallel to PQ.

As we know, the angles on the same side of the transversal are equal to 180°.

So, ?PQR + ?QRX = 180°

Or,?QRX = 180° – 110°

? ?QRX = 70°

Similarly,

?RST + ?SRY = 180°

Or, ?SRY = 180° – 130°

? ?SRY = 50°

Now, for the linear pairs on the line XY-

?QRX + ?QRS + ?SRY = 180°

Substituting their respective values we get,

?QRS = 180° – 70° – 50°

Or, ?QRS = 60°

Maths

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9th

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February 24, 2022

3. **In the Figure, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE**.

Joslin Smith

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Student

Solution:

Since AB || CD GE is a transversal.

It is given that ?GED = 126°

So, ?GED = ?AGE = 126° (alternate interior angles)

Also,

?GED = ?GEF + ?FED

As

EF ? CD, ?FED = 90°

? ?GED = ?GEF + 90°

Or, ?GEF = 126° – 90° = 36°

Again, ?FGE + ?GED = 180° (Transversal)

Substituting the value of ?GED = 126° we get,

?FGE = 54°

So,

?AGE = 126°

?GEF = 36° and

?FGE = 54°