1. QUESTIONS ON VOLUME AND SURFACE AREA FOR APTITUDE TESTS by : DR. T.K. JAIN AFTERSCHO ☺ OL centre for social entrepreneurship sivakamu veterinary hospital road bikaner 334001 rajasthan, india FOR – PGPSE / CSE PARTICIPANTS [email_address] mobile : 91+9414430763

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3. What is the length of the rod of maximum possible length which can be put in a room of dimensions : 20 * 30 * 40 m ? The formula of diagonal of cuboid is = sqrt (l^2+b^2+h^2) = sqrt ( 40^2+30^2+20^2) =sqrt(1600+900+400) =sqrt(2900) =53.85 meters answer

4. Area of the base of a rectangular tank is 6500 sq cm. volume of water in it is 2.6 cubic meters. What is the depth of this tank ? Height = volume / (length * breadth) let us convert volume into sq. Cm for ease in calculation = 2.6*100*100*100 = (2.6*100*100*100) /(6500) =400 cm or 4 meters

5. A cube has a surface area of 384 sq cm, what is its volume ? Surface = 6 * side ^2 side^2 = 384/6 = 64 side = 8 volume = 8^3 = 512 cubic cm answer

6. Three cubes of each of side of 4,6,8 are melted and then converted into one cube. What is the side of this new cube ? Volume of 1 st cube = 64, volume of 2 nd cube = 216 volume of 3 rd cube = 512 total volume = (64+512+216) =792 now let us find cubic root of 792 =9.25 answer

7. Length of a diagonal of a cube is 4*sqrt(3), what is the volume ? Formula of diagonal = sqrt(3) * side sqrt(3) * side = 4*sqrt(3) side = 4 volume = 64 answer

8. Each side of a cube is doubled, what is the impact on volume ? Formula of volume = side ^3 New side = (2a)^3 =8a^3 which is 8 times earlier volume so volume has increased 8 times. Answer

9. I want to make a box of size 10 * 20 * 30. What should be the area of the cardboard that I use for this (minimum) ? Answer = find total surface area of this box = 2 ( LB + LH+BH) =2(30*20 + 30*10+20*10) =2(1100) =2200 ANSWER

10. How many bullets (spherical) can you make from a cylinder of lead. Height, diameter of cylinder are 20,10 respectively ? Volume of cylinder / volume of sphere pi * r^2 * h / pi *4/3 *r^3 r=radius, pi = 22/7, h = height = (22/7 * 5*5*20 ) /( 4/3* 22/7* 5*5*5) = 3 answer

11. What is the volume, curved surface area, total surface area of a hemishpere of radius 7 cm ? Volume = 2/3*pi*radius^3 =2/3* 22/7 * 7*7*7 =718.67 curved surface area = ½ * total surface area of sphere = ½ * 4 pi * 7*7 =308 total surface area = 3 pi * r^2 =462

12. A cone, hemisphere and a cylinder have same base. Height is also same. What is the ratio of their volume ? Formula cone : 1/3 pi r ^2 h hemisphere = 2/3 pi r^3 cylinder = : pi r ^2 h ratio is : 1/3 : 2/3 : 1 =1:2:3 answer

13. A cone and a hemisphere have equal base and equal volume. What is the ratio of their height ? 1/3 pi r^2 h =2/3 pi r^3 1/3h = 2/3 r Height of cone is equal double the height of hemisphere answer

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