The circumference of a circular ground is 88m. A strip of land, 3m wide inside and along the circumference of the ground is to be levelled. What is the budgeted expenditure if the levelling cost is Rs 7 per square meter?
Answer: D Radius of the circular ground = (88*7)/ (2*22) = 14m Area of the ground to be levelled = pie* (142-112) = 22*75/7 Budgeted expenditure = (22*75/7)*7 = 22*75 = Rs. 1650
Q. No. 20:
An iron cube of 10 cm size is converted into a rectangular sheet of thickness 0.5cm. If the sides of the sheet be in the ratio 1:5, then the sides are
Answer: A Volume of a rectangular sheet =x*5x*0.5 Volume of iron cube =10*10*10=1000 Equating volume according to the given condition => 2.5*x*x = 1000 x=20 Thus, sides are 20 cm and 100 cm.
Q. No. 21:
If three equal cubes are placed adjacently in a row, then the ratio of the total surface area of the new cuboid to that of the sum of the surface area of the three cubes will be
Answer: D Let the side of one cube be 1cm, the Total surface area of cuboid = 2(lb+bh+hl) = 2(3+3+1) = 14 sq cm Sum of surface area of three cubes = 6*3 = 18 sq cm Required ratio = 14:18 => 7:9
Q. No. 22:
The radius and the height of a cylinder are equal to the radius of the sphere. If the ratio of the numerical values of the curved surface area of the cylinder and the volume of the sphere is 1:3, find the volume of the sphere.
Answer: A Let the radius of the sphere be r cm. The height and the radius of cylinder would be rcm each. Ratio of the curved surface area of the cylinder and the volume of the sphere => (2*pie*r*h) / (4*pie*r*r*r) = 1/3 : (2*pie *r*r)/(4/3 *r*r*r) = 1/3 => r=9/2 Volume of the sphere = 4/3 *pie*(9/2)3 = 4/3 *pie*729/8 = 243*pie/2
Q. No. 23:
The inside of a well thirty feet deep was given a finishing of brick-work. If the inner diameter of the well after the brick work, which was six inches thick, was completed was ten feet, what was the volume of the brick-work?
Answer: B Quantity of brick required =pie[(10/2 + 6/12)2-(10/2)2] *30 => 157.5*pie cubic feet.
Q. No. 24:
The cost of paving a floor with square tiles at Rs 7 per sq m is Rs 2240. If the length of the floor is twice the breadth, find the perimeter of the floor.
Answer: D Area of the floor = Total cost of paving the floor with square tiles / Rate of paving the floor with square tiles = 2240/7 = 320 sq m If the breadth of the floor is 'b' and the length of the floor is 'l' l=2b=> 320 =(2b)(b) =>b2=160 => b=4√10 l=2b = 8√10 perimeter of the floor = 2(l+b) = 2(4√10+8√10)= 24√10 m.