A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to
the base. At what height above the base the section has been made?
Statement (I): H = 20 cm
Statement (II): Volume of small cone: volume of large cone : 1:15
a. If the question can be answered with statement I alone but not statement II alone, or can be answered
with statement II alone but not statement I alone.
b. If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.
c. If the question can be answered with either statement alone.
d. If the question cannot be answered with the information provided.
A sphere of radius r is cut by a plane at a distance of h from its center, thereby breaking this sphere into two different pieces. The cumulative surface area of these two pieces is 25% more than that of the sphere. Find h.
Two mutually perpendicular chords AB and CD meet at a point P inside the circle such that AP = 6 cms, PB
= 4 units and DP = 3 units. What is the area of the circle?
a. 125pi/4 sq cms
b. 100pi/7 sq cms
c. 125pi/8 sq cms
d. 52pi/3 sq cms
Cylindrical cans of cricket balls are to be packed in a box. Each can has a radius of 7 cm and height of 30
cm. Dimension of the box is l = 76 cm, b = 46 cm, h = 45 cm. What is the maximum number of cans that can
fit in the box?
PQRS is a square of sides 2 cm & ST = 2 cm. Also, PT=RT. What is the area of trianglePST?
a. 2 cm2
b. Sq.rt(3) cm2
c. Sq.rt(2) cm2
d. 1/Sq.rt(2) cm2
A string is wound around two circular disk as shown. If the radius of the two disk are 40 cm and 30 cm
respectively. What is the total length of the string?
a. 70 cm
b. 70 + 165pi
c. 70 + 120pi
d. 70 + 165*(pi/2)
Figure below shows a box which has to be completely wrapped with paper. However, a single Sheet of paper need to be used without any tearing. The dimension of the required paper could be
a. 17 cm by 4 cm
b. 12 cm by 6 cm
c. 15 cm by 4 cm
d. 13 cm by 4 cm
An inverted right circular cone has a radius of 9 cm. This cone is partly filled with oil which is dipping from
a hole in the tip at a rate of 1cm2 /hour. Currently the level of oil 3 cm from top and surface area is 36pi cm2 . How long will it take the cone to be completely empty?
a. 216pi hours
b. 1 hour
c. 3 hours
d. 36pi hours
A square PQRS has an equilateral triangle PTO inscribed as shown: What is the ratio of Area of the triangle PQT to Area of the triangle TRU?
a. 1 : 3
b. 1 : Sq.rt(3)
c. 1 : sq.rt(2)
d. 1 : 2
A spherical shaped sweet is placed inside a cube of side 5 cm such that the sweet just fits the cube. A fly is
sitting on one of the vertices of the cube. What is the shortest distance the fly must travel to reach the sweet?
a. 2.5 cm
b. 5(Sq.rt(3) – 1) cm
c. 5(Sq.rt(2) – 1) cm
d. 2.5(Sq.rt(3) – 1) cm
Anil grows tomatoes in his backyard which is in the shape of a square. Each tomato takes 1 cm2 in his backyard. This year, he has been able to grow 131 more tomatoes than last year. The shape of the backyard
remained a square. How many tomatoes did Anil produce this year?
d. Insufficient Data
PQRS is a circle and circles are drawn with PO, QO, RO and SO as diameters areas A and B are shaded A/
B is equal to
ABCD is a square drawn inside a square PQRS of sides 4 cm by joining midpoints of the sides PQ, QR,
RS, SP. Another square is drawn inside ABCD similarly. This process is repeated infinite number of times.
Find the sum of all the squares.
a. 16 cm2
b. 28 cm2
c. 32 cm2
PQRST is a pentagon in which all the interior angles are unequal. A circle of radius ‘r’ is inscribed in each
of the vertices. Find the area of portion of circles falling inside the pentagon.
a. pi r2
b. 1.5pi r2
c. 2pi r2
d. 1.25pi r2
Three circles with radius 2 cm touch each other as shown :-
Find the area of the circle, circumscribing the above figure.