1.

A solid metal cylinder of 10 cm height and 14 cm diameter is melted and re-cast into two cones in the proportion of 3 : 4 (volume), keeping the height 10 cm. What would be the percentage change in the flat surface area before and after?

**Answer: Option 'D'**

**Let radius of cylinder, cone 1, cone 2 = R, r1, r2 respectively.
Let their volumes be V, v1, v2 respectively.
Cylinder is melted and recast into cone 1 & cone 2
So V = v1 + v2.
Ratio of volumes of the two cones v1 : v2 is 3 : 4.
If v1 is 3x, v2 will be 4x
Hence, volume of cylinder V= 7x
The volumes of the cylinder, cone 1 and cone 2 are πR**

2.

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

**Answer: Option 'D'**

**64√3 ^{2}
Area of an equilateral triangle = √3/4 S^{2}
If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm^{2};**

3.

Find the area of a parallelogram with base 24 cm and height 16 cm.

**Answer: Option 'D'**

**Area of a parallelogram = base × height = 24 × 16 = 384 cm ^{2}**

4.

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

**Answer: Option 'C'**

**The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 × 24 × 10 = 120 cm ^{2}
**

5.

A circular road is constructed outside a square field. The perimeter of the square field is 200 ft. If the width of the road is 7√2 ft. and cost of construction is Rs.100 per sq. ft., find the lowest possible cost to construct 50% of the total road.

**Answer: Option 'A'**

**What is to be found?
We have to find the lowest cost to construct 50% of the total road.
Data Given
A circular road is constructed outside a square field. So, the road is in the shape of a circular ring.
If we have to determine the lowest cost of constructing the road, we have to select the smallest circle that can be constructed outside the square.
Therefore, the inner circle of the ring should circumscribe the square.
Perimeter of the square = 200 ft.
Therefore, side of the square field = 50 ft.
The diagonal of the square field is the diameter of the circle that circumscribes it.
Measure of the diagonal of the square of side 50 ft = 50√2 ft.
Therefore, inner diameter of the circular road = 50√2.
Hence, inner radius of the circular road = 25√2 ft.
Then, outer radius = 25√2 + 722 = 32√2
The area of the circular road
= π r**

6.

If x units are added to the length of the radius of a circle, what is the number of units by which the circumference of the circle is increased?

**Answer: Option 'B'**

**Let the radius of the circle be 'r' units.
The circumference of the circle will therefore be 2 π r units.
If the radius is increased by 'x' units, the new radius will be (r + x) units.
The new circumference will be 2 π(r + x) = 2 πr + 2 πx
Or the circumference increases by 2πx units.**

7.

An order was placed for the supply of a carper 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 were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.

**Answer: Option 'B'**

**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
= 6x**

8.

A square sheet of paper is converted into a cylinder by rolling it along its length. What is the ratio of the base radius to the side of the square?

**Answer: Option 'D'**

**Surface area of the cylinder = Surface area of the square 2πh = a ^{2}
Here height 'h' of the cylinder = side of the square since it is rolled along its length.2πa = a^{2}
Base radius r = a/2π
Ratio of base radius to side of square = a/2π : a = 1/2π**

9.

The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?

**Answer: Option 'B'**

**Area of a triangle = r × s
Where r is the in radius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 × 28/2 = 35 cm**

10.

Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.

**Answer: Option 'A'**

**Area of a trapezium = 1/2 (sum of parallel sides) × (perpendicular distance between them) = 1/2 (20 + 18) × (15) = 285 cm ^{2}**

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