The perimeter of a right triangle is 72 cm and its area is 216 cm2. Find the sum of the lengths of its perpendicular sides. (in cm)
(1) 36
(2) 32
(3) 42
(4) 50
Find the area of the regular pentagon of side 6 cm and height 8 cm. (in cm2)
(1) 40
(2) 60
(3) 80
(4) 120
Find the perimeter of a sector of a circle if the angle and radius of it are 30° and 10.5 cm respectively.
(1) 26.5 cm
(2) 21.5 cm
(3) 23 cm
(4) 8 cm
The sides of a pentagonal prism are 10 cm, 12 cm, 15 cm, 8 cm and 6 cm. Its height is 14 cm. Find the total length of its edges.
(1) 172 cm
(2) 162 cm
(3) 182 cm
(4) 152 cm
Three cubes of sides 3 cm, 4 cm and 5 cm, respectively, are melted and formed into a larger cube. What is the side of the cube formed?
(1) 7 cm
(2) 6 cm
(3) 5 cm
(4) 4 cm
The sum of the length, breadth and the height of a cuboid is 20 cm and the length of its diagonal is 12 cm. Find the total surface area of the cuboid.
(1) 156 cm2
(2) 169 cm2
(3) 256 cm2
(4) 269 cm2
The radius of the base of a cone is 7 cm and its slant height is 25 cm. The volume of the cone is
(1) 3696 cm3
(2) 1232 cm3
(3) 2464 cm3
(4) 1864 cm3
The side of a square is equal to the diagonal of a cube. The square has an area of 1728 m2. Calculate the side of the cube.
(1) 12 m
(2) 24 m
(3) 27 m
(4) 36 m
The radius of the base and the slant height of a cone is 5 cm and 13 cm respectively. Find the volume of the cone.
(1) 88 π cm3
(2) 100 π cm3
(3) 92 π cm3
(4) 106 π cm3
If the ratio of the volumes of the spheres is 8 : 27, then the ratio of their surface areas is
(1) 4 : 9
(2) 9 : 4
(3) 4 : 3
(4) 2 : 9
The volume of a hemisphere is 1871 cm3. What is the total surface area of the hemisphere?
(1) 18 π cm2
(2) 27 π cm2
(3) 21 π cm2
(4) 24 π cm2
Find the volume of a regular octahedron of each edge 2 cm.
(1) 4 cm3
(2) 8 cm3
(3) 4 cm3
(4) 8 cm3
In a polyhedron, if the number of faces is 4 and the number of edges is 6, then the number of vertices of that polyhedron is
(1) 1
(2) 2
(3) 3
(4) 4
Fifteen identical spheres are made by melting a solid cylinder of 10 cm radius and 5.4 cm height. Find the diameter of each sphere.
(1) 6 cm
(2) 3 cm
(3) 2 cm
(4) 4 cm
Find the number of soaps of size 2.1 cm × 3.7 cm × 2.5 cm that can be put in a cuboidal box of size 6.3 cm × 7.4 cm × 5 cm.
(1) 14
(2) 12
(3) 13
(4) 11
If the radius of a sphere is increased by 25%, then the percentage increase in its volume is (approximately)
(1) 90%
(2) 95%
(3) 83%
(4) 78%
Find the volume of a hollow sphere of outer radius 9 cm and inner radius 6 cm.
(1) 342 π cm3
(2) 684 π cm3
(3) 36 π cm3
(4) 128 π cm3
A hollow hemispherical bowl of thickness 1 cm has an inner radius of 4.5 cm. Find the curved surface area of the bowl.
(1) 106π cm2
(2) 108π cm2
(3) 101π cm2
(4) 102π cm2
If the length of each edge of a tetrahedron is 18 cm, then the volume of the tetrahedron is
(1) 482 cm3
(2) 480 cm3
(3) 484 cm3
(4) 486 cm3
Find the total surface area of a regular octahedron, each edge of which is 10 cm.
(1) 100 cm2
(2) 200 cm2
(3) 300 cm2
(4) 400 cm2
The number of edges in a pyramid whose base has 20 edges is ______
(1) 10
(2) 20
(3) 30
(4) 40
A copper cable, 32 cm long, having a diameter 6 cm, is melted to form a sphere. Find the radius of the sphere.
(1) 6 cm
(2) 8 cm
(3) 10 cm
(4) 12 cm
The number of diagonals of a regular polygon in which each interior angle is 156°, is _______
(1) 24
(2) 54
(3) 90
(4) 45
ABCDEF is a regular hexagon. If AB is 6 cm long, then what is the area of triangle ABD?
(1) 8 cm2
(2) 12 cm2
(3) 15 cm2
(4) 18 cm2
The area and the radius of a sector are 6.93 sq. cm and 4.2 cm respectively. Find the length of the arc of the sector.
(1) 1.72 cm
(2) 0.86 cm
(3) 3.3 cm
(4) 6.6 cm
The perimeter of the base of a right prism, whose base is an equilateral triangle, is 24 cm. If its total surface area is (288 + 32)cm2, then its height is ______
(1) 10 cm
(2) 12 cm
(3) 14 m
(4) 14 cm
A large sphere of radius 3.5 cm is carved from a cubical solid. Find the difference between their surface areas.
(1) 224 cm2
(2) 140 cm2
(3) 176 cm2
(4) 80.5 cm2
If one of the edges of a regular octahedron is 4 cm, then find its height.
(1) 2 cm
(2) 4 cm
(3) 6 cm
(4) 2 cm
The dimensions of a cuboidal container are 12 cm × 10 cm × 8 cm. How many boetles of syrup can be poured into the container, if each bottle contains 20 cm3 of syrup?
(1) 46
(2) 54
(3) 48
(4) 58
A circle of radius 2 cm is inscribed in an equilateral triangle. Find the area of the triangle in cm2.
(1) 12
(2) 4
(3) 6
(4) 24
The circum-radius of a right triangle is 10 cm and one of the two perpendicular sides is 12 cm. Find the area of the triangle in sq. cm.
(1) 96
(2) 128
(3) 48
(4) 64
A parallelogram has two of its adjacent sides measuring 13 each. Find the sum of the squares of its diagonals.
(1) 169
(2) 338
(3) 676
(4) 507
A classroom is 5 m long, 2.5 m broad and 3.6 in high. If each student is given 0.5 m2 of the floor area, then how many cubic metres of air would each student get?
(1) 1.4
(2) 1.8
(3) 1.2
(4) 1.6
If the volume of a right equilateral triangular prism is 8500 dm3 whose height is 50 cm, then find the side of its base.
(1) 10 cm
(2) 10 dm
(3) 20 dm
(4) 20 cm
How many cubes, each of total surface area 54 sq.dm, can be made from a cube of edge 1.2 metre.
(1) 64
(2) 81
(3) 125
(4) 25
Four times the sum of the areas of the two circular faces of a cylinder is equal to the twice its curved surface area. Find the diameter of the cylinder if its height is 8 cm.
(1) 4 cm
(2) 8 cm
(3) 2 cm
(4) 6 cm
If the base of a right pyramid is a square of side 4 cm and its height is 18 cm, then the volume of the pyramid is ________
(1) 90 cm3
(2) 104 cm3
(3) 100 cm3
(4) 96 cm3
A right circular conical tent is such that the angle at its vertex is 60° and its base radius is 14 m. Find the cost of the canvas required to make the tent at the rate of ₹125 per m2.
(1) ₹15,400
(2) ₹30,800
(3) ₹16,400
(4) ₹32,800
A goat is tied to a corner of a rectangular plot of dimensions 14 in × 7 ni with a 21 in long rope. It cannot graze inside the plot, but can graze outside it as far as it is permitted by the rope. Find the area it can graze (in m2). (Take )
(1) 240
(2) 1560.5
(3) 1543.5
(4) 1232
If the breadth of a rectangle is increased by 5 cm, its area increases by 25 cm2. If its length is increased by 5 cm, its area increases by 20 cm2. Find the area of the rectangle (in cm2).
(1) 20
(2) 25
(3) 30
(4) 35
A cylinder-shaped tank is surmounted by a cone of equal radius. The height of the cone is 6 m and the total height of the tank is 18 m. Find the volume of the tank if the base radius of the cylinder is 5 m.
(1) 1650 m3
(2) 1100 m3
(3) 1244 m3
(4) 2200 m3
The radius of the cross-section of an inflated cycle tyre is 7 cm. The distance of the centre of the cross-section from the axle is 20 cm. Find the volume of air in the tyre.
(1) 19360 cm3
(2) 1760 cm3
(3) 6160 cm3
(4) 880 cm3
If h is the length of the perpendicular drawn from a vertex of a regular tetrahedron to the opposite face and each edge is of length s, then s2 is equal to ______
(1)
(2)
(3) h2
(4)
The radii of the ends of a frustum of a cone are 28 cm and 7 cm. The height of the cone is 40 cm. Find its volume.
(1) 32340 cm3
(2) 43120 cm3
(3) 10780 cm3
(4) None of these
The diagonal of a cube is 6 cm. Find its volume. The following arc the steps involved in solving the above problem. Arrange them in sequential order.
(A) ∴ Volume of the cube = a3 cm3 = (6)3 cm3 = 216cm3 .
(B) Then, diagonal of the cube = cm.
(C) From the given data = a= 6 cm.
(D) Let the side of the cube be a cm.
(1) DCBA
(2) DBCA
(3) DACB
(4) DBAC
Find the length of the arc of a sector of a circle whose angle at the centre is 120° and area of the sector is 462 cm2.
The following are the steps involved in solving the above problem. Arrange them in sequential order.
(A) Given. θ = 120°, area of the sector = 462 cm2. We know that A =
(B)
(C) Length of the arc of the sector =
(D) ∴ Length of the arc = 44 cm
(1) ABCD
(2) ACBD
(3) BACD
(4) BCAD
The radii of the top and the bottom of a metal can which is cone-shaped frustum, are 20 cm and 8 cm, respectively. The height of the can is 16 cm. Find the area of the metal sheet required to make the can with a lid.
The following are the steps involved in solving the above problem. Arrange them in sequential order.
(A) Area of metal sheet = πl(R + r) +πR2 +πr2
= π × 20(20 + 8) + π(20)2 + π(8)2.
(B) Given, R = 20 cm, r = 8 cm and h = 16 cm.
(C) = 20 cm.
(4) ∴ Area of the sheet = 1024 π sq. cm.
(1) BCAD
(2) ACBD
(3) BDAC
(4) BACD
The diagonal of a cube is 8 cm. Find its total surface area. The following are the steps involved in solving the above problem. Arrange them in sequential order.
(A) Then the diagonal of cube = a cm.
(B) ∴ Total surface area = 6a2 = 6(8)2 = 384 cm2.
(C) Let the side of cube be a cm.
(D) From the given data, a = 8 cm.
(1) ACBD
(2) CADB
(3) ABCD
(4) CBAD
The length of the diagonals of a rhombus are 10 cm and 24 cm. Find its side. (in cm)
(1) 10
(2) 13
(3) 12
(4) 11
Area of a right-angled triangle is 6 cm2 and its perimeter is 12 cm. Find its hypotenuse. (in cm)
(1) 5
(2) 6
(3) 7
(4) 8
A largest possible right-circular cylinder is cut out from a wooden cube of edge 7 cm. Find the volume of the wood left over after cutting the cylinder. (in cu cm)
(1) 73.5
(2) 82.5
(3) 76
(4) 92
A solid sphere of radius 4 cm is melted and recast into 'n' solid hemispheres of radius 2 cm each. Find n.
(1) 32
(2) 16
(3) 8
(4) 4
Three small metallic cubes whose edges are in the ratio 3 : 4 : 5 are melted to form a big cube. If big the diagonal of the cube so formed is 18 cm, then find the total surface area of the smallest cube. (in cm2)
(1) 154
(2) 184
(3) 216
(4) 162
A solid hemisphere of radius 8 cm is incited and recast into x spheres of radius 2 cm each. Find x.
(1) 4
(2) 8
(3) 16
(4) 32
In a triangle, the average of any two sides is 6 cm more than half of the third side. Find area of the triangle. (in sq. cm)
(1) 64
(2) 48
(3) 72
(4) 36
The lengths of the diagonals of a rhombus are 9 cm and 12 cm. Find the distance between any two parallel sides of the rhombus.
(1) 7.2 cm
(2) 8 cm
(3) 7.5 cm
(4) 6.9 cm
In a triangle, the sum of any two sides exceed the third side by 6 cm. Find its area (in sq. cm).
(1) 12
(2) 9
(3) 15
(4) 18
From each corner of a square sheet of side 8 cm. a square of side γ cm is cut. The remaining sheet is folded into a cuboid. The minimum possible volume of the cuboid formed is M cubic cm. If γ is an integer, then find M.
(1) 32
(2) 18
(3) 36
(4) 12