1.If the base of right rectangular prism remains constant and the measures of the lateral edges are halved, then its volume will be reduced by:
(a) 50%
(b) 33.33%
(c) 25%
(d) 66.66%
2.A conical tent has 60° angle at the vertex. The ratio of its radius and slant height is :
(a) 1 : 2
(b) 2 : 1
(c) 3 : 2
(d) 1 :3
3.If the volume of a cube is 512 cm^3, then its total surface area will be :
(a) 348 cm^2
(b) 256 cm^2
(c) 192 cm^2
(d) 384 cm^2
4.A curved surface of a cylindrical pillar is 264 m^2 and its volume is 924 m^3. The diameter of the pillar is :
(a) 12 m
(b) 10 m
(c) 14 m
(d) 16 m
5.The ratio of radii of two right circular cylinders is 2 : 3 and their heights are in the ratio 5:4.The ratio of their curved surface area is :
(a) 5 : 6
(b) 3 : 4
(c) 4 : 5
(d) 2 : 3
6.A cone, a hemisphere and a cylinder stand on equal base and have the same height. Their volumes are in the ratio:
(a) 1 : 3 : 2
(a) 2 : 3 : 1
(c) 1 : 2 : 3
(d) 3 : 1 : 2
7.The ratio of the areas of the incircle and the circumcircle of a square is :
(a) 1 : 2
(b) 2 : 3
(c) 3 : 4
(d) 4 : 5
8.The height of a solid right circular cylinder is 6 metres and three times the sum of the areas of its two end faces is twice the area of its curved surface. The radius of its base, in metre is :
(a) 4
(b) 2
(c) 8
(d) 10
9.The ratio of the volume of a cube to that of a sphere, which will exactly fit inside the cube is :
(a) 2 : π
(b) π ∶ 6
(c) 6 : π
(d) 8 : π
10.A cube of sides 3 cm is melted and smaller cubes of sides 1 cm each are formed. How many such cubes are possible?
(a) 21
(a) 23
(c) 25
(d) 27
ANSWERS AND SOLUTION
1.(a) Volume of prism = base area * height = A * h
so new volume = A * h/2
{height = h/2}
so % decrease in volume = (Ah – Ah)/2/Ah * 100 = 1/2 * 100 = 50%
2.(a)
3.(d) Let side of the cube = a
so v = a^3 = 512=> a = 8 cm
so Total surface area = 6a^2
= 6 * 64
= 384 cm^2
4.(c)Let ‘r' be the radius of base and h be the height of the cylinder,
then;
2πrh = 264 => rh = 132/π and πr^2h = 924 => r = 7
2r = 14m
5.(a) First cylinder Second cylinder
r1 = 2r r2 = 3r
h1 = 5h h2 = 4h
so Required ratio = 2πr1h1 : 2πr2 h2
= 2 * 5 : 3 : 4
= 5 : 6
6.(c) Required ratio
= 1/3 π^2h : 2/3 πr^2h : πr^2h
(height of cone= height of hemisphere = r)
= 1/3 : 2/3 : 1 = 1 : 2 : 3
7.(a) If the length of the side of square be a units, then
Radius of incircle = a/2
Radius of circum – circule = √2a/2= a/√2
so Required ratio = π × (a/2)^2 ∶ π × (a/√2)^2
= 1/4 : 1/2 = 1:2
8.(a)Let the radius of the base be r metre.
so 3 * 2πr^2 = 2 * 2 πrh => 3r = 2h
=> 3r = 2 * 6
=> r = 4 metre
9.(c) If the edge of cube be x units then diameter of sphere = x units
so Radius of sphere = x/2
so Required ratio = x^3 : 4/3 π x^3/8 = 6∶ π
10.(d)
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