1) A square pyramid of height 5 m is attached to the top face of the cubical box of side 8 metres, such that the pyramid exactly covers the top face of the cubical box. Find the visible surface area of the combined structure excluding the base of the cubical box.
a) 16(10 + √41) m2
b) 4(10 + √39) m2
c) 16(16 + √41) m2
d) 12(16 + √41) m2
e) None of these
2) The ratio of length and breadth of a cuboid is 4:3 respectively, and ratio of breadth and height is 8:4 respectively. If the surface area of cuboid is 720 m2 then find the volume of a cube having side equal to the breadth of the cuboid.
a) 1000 m^3
b) 1331 m^3
c) 1728 m^3
d) 2744 m^3
e) 3375 m^3
3) The ratio of the volume of a cone and the volume of a cylinder of same base is 5 : x respectively. If the height of the cone is 45 cm, and the total surface area of a structure made by joining the same cone and cylinder such that the base of both cone and cylinder completely coincide, is 11340 cm2 then find the value of x, if the radius of cone is 28 cm. (use pie = 3)
a) 4
b) 6
c) 9
d) 12
e) None of these
4) A hollow cylindrical sheet has radius of 8 cm and its height is 4 cm more than the radius. The cylindrical sheet is cut in such a way that it forms a single rectangular sheet which has a breadth equal to the height of the cylinder. If a smaller rectangular sheet of breadth 2 cm and length equal to 5% of the length of the sheet formed is cut out, then find the number of smaller sheets that can be cut out from the sheet which is formed from the cylindrical sheet. (Use pie = 3)
a) 119
b) 117
c) 114
d) 120
e) None of these
5) A cuboidal box whose sides are in the ratio 12 : 11 : 9 is filled with ice cream. Ice cream is equally distributed to 72 persons in a cone from that box. The ice cream is filled in each cone in such a way that at the top of cone ice cream forms a hemisphere of same radius as that of cone. If height of cone and hemisphere is 8 cm and 3 cm respectively, then find the difference between the largest side and smallest side of the cuboidal box.
a) 8 cm
b) 6 cm
c) 12 cm
d) 15 cm
e) None of these
6) Two circles are drawn in such a way that radius of first circle is equal to the side ot a square and radius of second circle is equal to the diagonal of that square. Find the ratio ot perimeter of third circle whose area is the sum of area of first and second circle together to the perimeter of the square.
a) 3π : 2
b) π : 2
c) √3 : 2
d) π√3 : 2
e) None of these
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