SSC CGL 201911)N solid metallic spherical balls are melted and recast into a cylindrical rod whose radius is 3 times that of a spherical ball and height is 4 times the radius of a spherical ball. The value of N is:
27
N volume of solid metallic spherical balls = volume of cylindrica; \(N {\times4\over3}\pi{r}^3= \pi(3r)^2\times4r\);
=\(N {\times4\over3}\pi{r}^3= 36\pi{r}^3\);
N= 27
SSC CGL 201912)The radius of the base of a right circular cylinder is increased by 20%. By what percent should its height be reduced so that its volume remains the same as before?
\(30\frac{5}{9}\)
Let the height be reduced by x%. r1 = 1.2r; h1 = \({(100-x)h\over100}\); \(\pi r^2h=\pi(1.2r)^2\times{(100-x)h\over100}\); \(x={44\over1.44}={30\frac{5}{9}}\)
SSC CGL 201913)The radius and the height of a right circular cone are in the ratio 5 : 12. Its curved surface area is 816.4\(cm^2\) , What is the volume (in \(cm^3\)) of the cone? (Take \(\pi =3.14\))
2512
SSC CGL 201914)The base of a right pyramid is an equilateral triangle with area \(16\sqrt3cm^2\) . If the area of one of its lateral facesis 30 \(cm^2\) , then its height (in cm.) is :
\(\sqrt{611\over12}\)
SSC CGL 201915)A sphere of maximum volume is cut out from a solid hemisphere. What is the ratio of the volume of the sphere to that of the remaining solid?
1 : 3
SSC CGL 201916)A right prism has height 18 cm and its base is a triangle with sides 5 cm, 8 cm and 12 cm. What is its lateral surface area (in \(cm^2\)) ?
450
SSC CGL 201917)A 15 metre deep well with radius 2.8 metre is dug and the earth taken out from it is spread evenly to form a platform of breadth 8 metre and height 1.5 metre. What will be the length of the platform? (Take \(\pi={22\over7}\))
30.8 metre
Height of the well H = 15 m and radius of the well r = 2.8 m
Let the length of the platform be l m
Breadth of the platform b = 8 m
Height of the platform h = 1.5 m
According to the question
lbh = πr2h
l × 8 × 1.5 = (22/7) × 2.8 × 2.8 × 15
⇒ l = 30.8 m
SSC CGL 201918)A tank is in the form of a cuboid with length 12 m. If 18 kilolitre of water is removed from it, the water level goes down by 30cm. What is the width (in m) of the tank?
5
Let the length of the tank = 12 m
Height of the tank = 30 cm = 30/100 m = 0.3 m
Let the width of the tank be w m
According to the question
12 × b × 0.3 = 18
b = 5m
SSC CGL 201919)The radius of the base of a right circular cylinder is 3 cm and its curved surface area is 60\(\pi cm^2\) , The volume of the cylinder (in \(cm^3\)) is:
\(90\pi\)
SSC CGL 201920)A solid cylinder of base radius 12 cm and height 15 cm is melted and recast into n toys each in the shape of a right circular cone of height 9 cm mounted on a hemisphere of radius 3 cm. The value of n is:
48