Surface Area & Volumes
Take = 22/7, unless stated otherwise. ，
3Q-1 What is the surface area of a cube whose volume is 64 cm?
Q-2 A wooden solid sphere of radius r cm is divided into two equal parts. What is the whole surface area of the two parts?
2Q-3 If the curved surface area of a right circular cylinder is 1760 cm and its radius is 21 cm, then
what is its height?
3Q-4 Two cubes each of volume 64 cm are joined face to face. What is the surface area of the
resulting cuboid ?
Q-5 How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius 8 cm ?
Q-6 The diameter of a metallic sphere is 6 cm. It is melted and drawn into a wire having diameter of the cross-section as 0.2 cm. Find the length of the wire?
Q-7 What is the height of a cone whose base area and volume are numerically equal?
Q-8 A rectangular piece of paper of dimensions 60 cm X 88 cm is rolled to form a hollow circular cylinder of height 60 cm. What is the radius of the cylinder?
Q-9 In the adjoining figure, the bottom of the glass has a hemispherical raised portion. The glass is fitted with orange juice. How much juice a person will get?
Q-10 Two right circular cones X & Y are made, X having three times the radius of Y and Y having half the volume of X. Calculate the rates of X & Y?
2/3 marks Questions
2. Find the volume of the cone given that its base Q-1 The curved surface area of a cone is 550 cm
diameter is 14 cm.
Q-2 A square field and an equilateral triangular park have equal perimeters. If the cost of ploughing 2the field at the rate of Rs. 5 per m is Rs. 720, find the cost of maintaining the park at the rate of Rs. 10 2per m.
Q-3 An iron solid sphere of radius 3 cm is melted and recast into small spherical balls of radius 1 cm each. Assuming that there is no wastage in the process, find the number of small spherical balls made from the given sphere?
Q-4 A rectangular water tank of base 11 cm X 6 cm contain water up to height of 5 m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of water level to be raised in this tank?
Q-5 The base radii of two circular cones of the same height are in the ratio 3:5. Find the ratio of their volumes.
Q-6 Circumference of the edge of hemispherical bowl is 132 cm. Find the capacity of the bowl.( = ，
Q-7 In the given figure, a cone of radius 10 cm is divided into two parts by drawing a plane through the mid-points of its axis, parallel to its base. Compare the volume of the two parts?
Q-8 Find the volume of the largest right circular cone that can be cut out of a cube whose radius is 9 cm.
Q-9 50 circular plates, each of radius 10.5 cm and thickness 1.6 cm, are placed one above the other to form a solid circular cylinder. Find the curved surface are and volume of the cylinder so formed?
Q-10 the radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm
2respectively. It is melted and recast into a solid right circular cylinder of height 10 cm. Find the 3
diameter of the base of the cylinder.
22 2 2 1) 16？ cm 2) 3？ r cm 3)13.3 cm 4) 160 cm
5) 512 6)9 m 7) 3 units 8) 14 cm
39) 396？cm 10) H/h=1/18
2/3 marks questions
31) 1334.66 cm 2) Rs. 4428.80 3) 27 4) 8.57m
33 5) 9:25 6) 19104 cm 7)1:7 8)190.93 cm
239) (5280 cm, 27720 cm) 10) r=3.5 cm, d=7 cm
Q1. The given distribution shows the number of runs scored by some top batsman of the world in one
day international cricket matches.
RUNS SCORED NUMBER OF
Find the mode of the data.
Q2. Give the empirical relation between median, mode and mean.
Q3. If the median of the distribution given below is 28.5. Find the value of ‘x’ and ‘y’.
Q4. Find the median of the following frequency distribution
100 200 300 400 500 600 700 800 900 1000 FREQUENCY 2 5 9 12 17 20 15 9 7 4
Q5. The median of the following data is 20.75. Find the missing frequencies ‘x’ and ‘y’ . If the total
frequency is 100.
CI 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 FREQUENCY 7 10 x 13 y 10 14 9
Q6. If the mean of the following distribution is 6, find the value of’p’.
X 2 4 6 10 P+6 Y 3 2 3 1 2
(1) 4608.7 runs
(2) Mode = 3 median – 2 Mean
(5) y = 20 , x = 17
(6) P = 7
(1) 5 cm
1. All questions are compulsory.
2. Section A consists of 10 questions of 1 mark each.
Section B consists of 5 questions of 2 marks each.
Section C consists of 10 questions of 3 marks each.
Section D consists of 5 questions of 6 marks each.
3. There is no overall choice however internal choice has been provided.
1. State fundamental theorem of arithmatic.
2. One card is drawn at random from a well shuffled deck of 52 cards.
Find the probability of getting a king of red suit.
represent inte rsecting lines then find the 3. If kx+y=7 and 3x-2y=11
value of K.
4.Find the 18th term of A.P. 2,32,52,........ o5. If sec5A=cosec(A-36),where 5A is an acute angle. Find the value of A.6. If mode of the following data is 15. Find K.
7. In the given fig DE is parallel to BC.
AD2If and AC=18 cm. Find AE.？BD3
8. Find X in the give n fig. if PT is tangent to the circle.
29. and are zeros of 25(2), then find the product of and .Ifxx，！，！;；
2210. Find the perimeter of a quadrant of circle of radius 7cm(=).，2
11. Find 31 term of an AP whose 11 term is 38 and 16 term is 73. 12. Find the ratio in which the y-axis divides the join of (5,-6) and(-1,-4).
Also find the point of intersection.
13. Evaluate without using trignometric table
IfAecAsec4cos(20),where 4A is an acute angle, ？；
find the value of A.
14. If AB,AC and PQ are tangents in the given fig. and AB=5 cm.
Find the perimeter of APQ.
15. If the mean of the following data is 18. find the missing frequency P.
X 10 15 20 25 i
f 5 10 p 8 i
16. Find the zeros of polynomial p(x)=2322 and xx；；
verify the relationship between the zeros and co-efficients.
On dividing x-3x+x+2 by the polynomial g(x), the quotient
and remainder were x-2 and -2x+4 respectively. Find g(x).17. Find the value of K for which (k-3)x+3y=K, kx+ky=12 will
have infinitely many solutions.
18. The hypotenuse of a right triangle is 1 m less than twice the
shortest side. If third side is 1 m more than the shortest side.
Find the sides of the triangle.
19.Construct a triangle of sides 4cm, 5cm & 6cm, and then a triangle
2similar to it whose sides are of corresponding sides of first triangle.3
20. Prove that:
21.he mid points of the sides of a triangle are (3,4), (4,6) and(5,7).T
Find the co-ordinates of the vertices of the triangle.22. How many coins 1.75 cm in diameter and 2mm thick must be melted to form a cuboid 11cm X 10 cmX 7cm.
23.Prove that 5 -32 is an irrational number.
BC324. In a trapezium ABCD, ABCD and CD=2 AB Cuts AD in F and BC in E, such that .？EC4
Diagonal BD intersect EF at G. Prove that 7EF=10AB.
1125. Prove that the points(a,0),(0,b) and (1,1) are collinear if 1.;？ab
SECTION-D26.Prove that the ratio of areas of two similar triangles is equal to the ratio
of squares of their corresponding sides using the above theorem do the
The area of two similar triangles ABC and PQR are in the ratio 9:16,. If BC=4.5 cm.
Find the length of QR.
State and prove Pythagoras theorem. Using the above theorem, Prove the following. 222In the given figure PQR is a right triangle right angled at Q. If QS=SR, show that PR=4PS-3PQ.
27. A sailor can row a boat 8 km downstream and return back to the starting point in 1 hr. 40min. If speed of stream is 2 km/hr. Find the speed of boat in
28. An aeroplane when 3000m high, passes vertically above another aeroplane at an instant when the angles of elevation of the two
00 0 and 45 respectively. aeroplanes from the same point on the ground are 6
Find the vertical distance between two aeroplanes.
29. A solid in the form of right circular cylinder, with hemisphere at one end and a cone at other end. the radius of the common base is 3.5 cm and
the heights of the cylindrical & conical portion are 10cm amd 6 cm respectively.
22， Find the total surface area of the (use =)7
30. Calculate Medians of the following data:
Marks obtained No. of students Less than 20 0 Less than 30 4 Less than 40 16 Less than 50 30 Less than 60 46 Less than 70 66 Less than 80 82 Less than 90 92 Less than 100 100