Mathematics Mcqs

A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?

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A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?

A. 45 cm
B. 18 cm
C. 90 cm
D. None of these

Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h = 9 cm

The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?

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The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?

A. 2 : 5
B. 1 : 5
C. 3 : 5
D. 4 : 5
The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5

The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?

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The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?

A. Rs. 4800
B. Rs. 3600
C. Rs. 3560
D. Rs. 4530
Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) – (6 * 3) – 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs. 4530

A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?

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A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?

A. 10
B. 100
C. 1000
D. 10000
Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000

There are two circles of different radii. The area of a square is 196 sq.cm, whose side is half the radius of the larger circle. The radius of the smaller circle is three-seventh that of the larger circle. What is the circumference of the smaller circle ?

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There are two circles of different radii. The area of a square is 196 sq.cm, whose side is half the radius of the larger circle. The radius of the smaller circle is three-seventh that of the larger circle. What is the circumference of the smaller circle ?

A. 12 π cm
B. 16 π cm
C. 24 π cm
D. 32 π cm
Radius of larger circle
= 2×196−−−√=28cm
Circumference of smaller circle
= (37×28)cm=12cm
Circumference of smaller circle
= 2πr=2π×12= 24πcm

The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?

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The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?

A. 23.57 cm
B. 47.14 cm
C. 84.92 cm
D. 94.94 cm
Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places

A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is__________?

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A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is__________?

A. 3.34
B. 2
C. 4.5
D. 5.5
Area of the path = Area of the outer circle – Area of the inner circle = ∏{4/2 + 25/100}2 – ∏[4/2]2
= ∏[2.252 – 22] = ∏(0.25)(4.25) { (a2 – b2 = (a – b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m

The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.

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The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.

A. 4192 sq m
B. 4304 sq m
C. 4312 sq m
D. 4360 sq m
Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 – ∏s2
= ∏{1762/∏2 – 1322/∏2}
= 1762/∏ – 1322/∏
= (176 – 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m

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.

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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.

A. 200 sq cm
B. 72 sq cm
C. 162 sq cm
D. Cannot be determined
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.