Answer: A Total surface area of cone = Pie*r(l+r) Where, l is the slant height, l =(r2+h2)1/2 Therefore,on putting r= 30 and h =40 cm. Total surface area = 7543 cm2
Q. No. 20:
A spiral is made up of 13 successive semicircles, with center alternatively at A and B, starting with center at A. the radii of semicircles, thus developed are 0.5cm, 1cm, 1.5cm, and 2cm and so on. The total length of the spiral is
Answer: A As per the question there are 13 successive semi-circles with radii 0.5cm, 1cm......... Total length of the spiral = Pie*0.5 + pie*1+pie*1.5..............Pie *6.5 => pie(0.5+1+1.5+.........6.5) = 22/7 * 7/2*13 = 143 cm.
Q. No. 21:
A cylinder, a hemisphere and a cone stand on the same base and have the same heights. The ratio of the areas of their curved surface is:
Answer: D Let the three solids have base radius and height of x units. The curved surface areas of the three solids are: Cylinder = 2*pie*x*x Hemisphere = 2*pie*x*x Cone :- pie*x* (Slant height) = Pie*x*√2*x Hence the ratio is √2 : √2 : 1
Q. No. 22:
A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?
Answer: B Let of original rectangle length = x and breadth = 2 Thus, Ratio = x/2.....(i) If it is cut then its length = 2 and breadth = x/2 Thus, ratio = 2/(x/2) = 4/x........(ii) Eq(1) is equal to eq(2){According to question} x/2 = 4/x Thus B is the correct option.
Q. No. 23:
PQR is an equilateral triangle and a circle is inscribed it, touching all the three sides. If area of triangle PQR = 1.5√3 sqcm, find the area of the inscribed circle.
Answer: B Let the area of equilateral triangle = √3/4 * a2 = 1.5√3 a = √6 cm. Altitude of the equilateral triangle is √3/2 * a = √18/2 cm Radius of inscribed circle is => (Altitude)/3 = √18/6 cm Area of circle = pie * (√18/6)2 = pie/2.
Q. No. 24:
It took 15 hour and 40 min for Rakesh to paint four walls and the ceiling of a room of size 900 cu ft. The ceiling height of the room is 10ft. If Rakesh is painted at a constant rate of 0.5 ft/min, how long will it take for him to paint the walls ?
Answer: A Rakesh paints 0.5 sq. ft in 1 min. Rakesh paints 470 sq. ft in 15 hour and 40 minutes. Thus, the dimensions of the room is (10*10*9) Cu ft. Area of 4 walls = 380 sq. ft Time taken to paint it = 12 hours and 40 minutes.