SSC CGL 201931)A hemispherical bowl of internal diameter 36 cm is full of a liquid. This liquid is to be filled into cylindrical bottles each of radius 3 cm and height 12 cm. How many such bottles are required to empty the bowl?
36
SSC CGL 201932)A solid cube is cut into three cuboids of same volumes. What is the ratio of the surface area of the cube to the sum of the surface areas of any two of the cuboids so formed?
9 : 10
SSC CGL 201933)If the curved surface area of a solid cylinder is one-third of its total surface area, then what is the ratio of its diameter to its height?
4 : 1
SSC CGL 201934)If the volume of a sphere is 4851 \(cm^3\), then its surface area (in \(cm^2\)) is: (Take \(\pi={22\over7}\))
1386
\(V = {4\over 3} \pi r^3 = \) 4851 ;
r = \({21\over 2} cm\) ;
S.A = \(4 \pi r^2\) = 1386 sqcm
SSC CGL 202035)The volumes of spheres A and B are in the ratio 125 : 64. If the sum of radii of A and B is 36 cm,then the surface area (in \(cm^2\)) of A is:
\(1600\pi\)
Let, radius of sphereA = R cm; Radus of sphere B = r cm; so \({{4\over3}\pi{R}^3}\over{{4\over3}\pi{r}^3}\) = \(125\over64\);
\({R^3\over r^3 }=({5\over4})^3\) ; \({R\over r} = {5\over4} = 5: 4\); and R + r = 36 cm; R = \({5\over9}\times36 = 20 cm\);
Surface area of sphere A = \(4\pi{R}^2= 4\pi\times(20)^2=1600\pi {cm}^2\)
SSC CGL 202036)Find the height of a cuboid whose volume is 330 \(cm^3\) and base area is 15 \(cm^2\) .
22 cm
Volume of cuboid = Base area x height
330 = 15 x height
Height = 330/15 = 22 cm
SSC CGL 201637)A cylinderical container of 32 cm height and 18 cm radius is filled with sand. Now all this sand is used to form a conical heap of sand. If the height of the conical heap is 24 cm, what is the radius of its base?
36 cm
SSC CGL 202038)If the radius of a right circular cylinder is decreased by 10%, and the heightis increased by 20%, then the percentage increase/decrease in its volume is :
decrease by 2.8%
Volume of right circular cylinder =\( \pi r^2h\);
Radius of a right circular cylinder is decreased by 10%, and the height is increased by 20% so,
r1 =\( r \times 90/100 = 0.9r\) ;
h1 = \(h \times 120/100 = 1.2h\) ;
Volume of new right circular cylinder =\(\pi r1^2h1 = \pi (0.9r)^2(1.2h) = 0.972(\pi r^2h)\) ;
Decrements in volume =\( \pi r^2h - 0.972(\pi r^2h) = 0.028(\pi r^2h)\) ;
Percentage Decrements in volume = \(\frac{0.028(\pi r^2h)}{(\pi r^2h)} \times 100\) = 2.8%
SSC CHSL 202139)The length of a rectangle is five times of its breadth. If the area of the rectangle is 3125 cm2, then what is the length of the rectagle?
125 cm
SSC CHSL 202140)The sum of the radius of the base and the height of a closed solid cylinder is 12.5 cm. If the total surface area of the cylinder is 275 cm2, then its radius is: \(\rm \left(Take \space\pi = \frac{22}{7}\right)\)
3.5 cm