SSC CGL 201911)The volume of a right pyramid is \( 45\sqrt{3} cm^3\) and its base is an equilateral triangle with side 6 cm. What is the height(in cm)of the pyramid?

Correct Option: A

15

Side of equilateral triangle = 6 cm;

Area of equilateral triangle =\( \frac{\sqrt{3}}{4}a^2 = \frac{\sqrt{3}}{4}6^2 = 9\sqrt 3\);

The volume of a right pyramid = \(45\sqrt{3} cm^3; \frac{1}{3}9\sqrt 3h = 45\sqrt{3} cm^3;\)

h = 15 cm

SSC CGL 201912)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:

Correct Option: B

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 201913)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?

Correct Option: C

\(30\frac{5}{9}\)

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 201914)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 \(\pi =3.14\))

Correct Option: A

2512

SSC CGL 201915)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 :

Correct Option: C

\(\sqrt{611\over12}\)

SSC CGL 201916)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?

Correct Option: C

1 : 3

SSC CGL 201917)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 \(cm^2\)) ?

Correct Option: A

450

SSC CGL 201918)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 \(\pi={22\over7}\))

Correct Option: D

Length of the platform is 30.8 m

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 = πr^{2}h

l × 8 × 1.5 = (22/7) × 2.8 × 2.8 × 15

⇒ l = 30.8 m

Length of the platform is 30.8 m

SSC CGL 201919)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?

Correct Option: B

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 201920)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:

Correct Option: A

\(90\pi\)

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