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Mensuration

Important Instructions
51.

If circumference of circle is 82π then value of 'r' is

Answer: A

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52.

Formula used to measure circumference of circle is

Answer: A

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53.

A circle is inscribed in a square. If the difference between area of the square and circle is 262.5 cm⊃2;, then find the area of the rectangle whose perimeter is same as that of circle while length of rectangle is 20% more than the breadth of rectangle (in cm⊃2;). 

Answer: D

Let the side of square be 2a.
So, the diameter of circle = 2a
Radius of circle = a

WKT, Area of square = 4a
Area of circle = π r⊃2;
Perimeter of circle = 2π r
Area of rectangle = l x b
Perimeter of rectangle = 2(l + b)
Given that difference between area of the square and circle is 262.5 cm⊃2;.
Area of square - Area of circle = 262.5
4a⊃2; - (22/7)a⊃2; = 262.5
28a⊃2; - 22a⊃2; = 1837.5
6a⊃2; = 1837.5
a⊃2; = 306.25
a = 17.5 cm

Perimeter of circle = 2πa = 2 x (22/7) x 17.5 = 110 cm

Also given length of rectangle is 20% more than the breadth of rectangle.
Let the breadth of rectangle be X.
So, length of rectangle = (120/100)X = 1.2X
As per the question,
Perimeter of rectangle = Perimeter of circle
2(1.2X + X) = 110
2.4X + 2X = 110
4.4X = 110
X = 25 cm
Breadth of rectangle = 25 cm
Length of rectangle = 1.2(25) = 30 cm

Area of rectangle = 25 x 30 = 750 cm⊃2;.

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54.

Baskin n Robbin’s biggest ice-cream cardboard cone has height of 24 cm and slant height of 25cm. One sheet of cardboard makes 8 such cones. What is area of the sheet?

Answer: A

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55.

A solid rubber sphere weighs 6kg when its diameter is 6cm.  Using the same material, a hollow sphere is made with outer diameter 18cm and inner diameter 12 cm. What is its weight?

Answer: A

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56.

The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.

Answer: D

Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 

4a = 2(l + b) 

2a = l + b 

l . b = 480 

We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found . 

Area of the square cannot be found.

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57.

Formula used to measure area of circle is

Answer: B

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58.

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

Answer: A

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;

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59.

Find the number of bricks, each measuring 24 cm×12 cm × 8 cm, required to construct a wall 24 m long, 8m high and 60 cm thick if 10% of the wall is filled with mortar?

Answer: C

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60.

Which of the following is equal to 1 kilolitre?

Answer: D

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