481. The length of a rectangle is two – fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
482. Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
A. 225 sq.m
B. 360 sq.m
C. 600 sq.m
D. 480 sq.m
483. The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
A. 81 : 121
B. 9 : 11
C. 729 : 1331
D. 2. 7 : 12
484. 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
485. 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
486. The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
A. 252 m
B. 704 m
C. 352 m
D. 808 m
In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m
487. 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
488. 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?
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
489. 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
Circumference of smaller circle
Circumference of smaller circle
= 2πr=2π×12= 24πcm
490. 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
Circumference of the semicircle
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
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