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Volume Calculation - Solved Examples
Q 1 - The diagonal of a cube is 12√6m .Find its surface area.
Answer - B
Explanation
Let the edge of the cube be X. √(3 )X=12√(6) ⇒ X=12√(2) Surface area = 6X2 = (6 x 12√(2) x12√(2)) m2 ≡ 1728 m2.
Q 2 - The surface area of a cube is 1728 cm2. Find its volume.
Answer - A
Explanation
Let the edge of the cube be X. Then, 6X2 = 1728 ⇒ X2 = 288 ⇒ X = 12√2 cm. Volume = X3 = (12√2)3 cm3 = 3456√2 cm3.
Q 3 - Find the number of bricks, each measuring 24 cm x 12 cm x 8 cm, required to construct a wall 24 m long, 8m high and 60 cm thick.
Answer - A
Explanation
Volume of the wall = (1800 x 600 x 90) cm3. Volume of 1 brick = (36 x 18 x 12) cm3. Number of bricks=((1800 x 600 x 90)/( 36 x 18 x 12)=12500
Q 4 - A right triangle with sides 6 cm, 8 cm and 10 cm is rotated the side of 6 cm to form a cone. The volume of the cone so formed is:
Answer - B
Explanation
We have R = 6 cm and H = 8 cm. Volume = (1/3)πR2H= (1/3)πx62x8=96π cm3
Q 5 - A room is 30 m long and 24 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
Answer - C
Explanation
Let the height be H 2(30 + 24) x H = 2(30 x 24) ⇒ H=(2(30 x 24))/(2(30 + 24))=(30 x 24)/54=40/3 m ⇒ Volume = 30 x 24 x 40/3 = 9600 m3
Q 6 - A hollow steel pipe is 42 cm long and its external diameter is 16 cm. If the thickness of the pipe is 2 cm and steel density weighs 12 g/cm3, then the weight of the pipe is:
Answer - A
Explanation
External radius = 8 cm, Internal radius = 6 cm. Volume of steel = ( π x (82-62) x42) =1176 π cm3 Weight of steel = (1176 π x 12) gm = 51744 gm = 51.744 kg.
Q 7 - Find the area of right circular cone curved surface if slant height is 20 m and height is 16 m.
Answer - D
Explanation
L = 20 m, H = 16 m. So, R = √(L2-H2) = √(202-162) = 12 m. ⇒ Curved surface area = πRL = (π x 12 x 20) m2 = 240π m2.
Q 8 - Find the volume & curved surface area of a cylinder with diameter of base 14 cm and height 60 cm.
Answer - D
Explanation
Volume = πR2H= π x 72 x 60 = 9240 cm3 Curved surface area = 2πRH = (2 π x 7 x 60) cm2 =2640 cm2
Q 9 - If the volume of a cylindrical tank is 3696 m3 and the diameter of its base is 28 m, then find the depth of the tank.
Answer - B
Explanation
Let the depth of the tank be H meters. Then, Volume = πR2H= π x 142 x H = 3696 m3 ⇒ H=6 m
Q 10 - How many steel rods, each of length 14 m and diameter 4 cm can be made out of 1.76 cm3 of steel?
Answer - B
Explanation
Volume of 1 rod = (( 22/7) x (2/100) x (2/100) x 14 ) m3= 11/625 m3 Volume of steel = 1.76 m3 Number of rods = (1.76 x 625/11) = 100.
Q 11 - Find the volume and surface area of a Box 32 m long, 28 m broad and 14 m high.
Answer - A
Explanation
Volume = (32 x 28 x 14) m3 = 12544 m3. Surface area = [2 (32 x 28 + 28 x 14 + 32 x 14)] m2 = (2 x 1736) m2 = 3472 m2.
Q 12 - Find the length of the longest pole that can be placed in a room 24 m long 16 m broad and 18 m high.
Answer - A
Explanation
Length of the longest pole=√(242+162+182)=34 m
Q 13 - A wheel makes 2000 revolutions in covering a distance of 44 km. Find the radius of the wheel.
Answer - B
Explanation
Distance covered in one revolution = ((44 X 2000)/1000) = 88m. 2πR = 88 2 x (22/7) x R = 88 ⇒ R = 88 x (7/44) = 14 m.
Q 14 - A rectangular block 35 cm x 42 cm x 70 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.
Answer - A
Explanation
Volume of the block = (35 cm x 42 cm x 70 cm) cm3 = 300x73 cm3. Side of the largest cube = H.C.F. of 35 cm , 42 cm and 70 cm = 7 cm. Volume of this cube = (7 x 7 x 7) cm3 = 73 cm3. Number of cubes = 300x73/73 = 300.
Q 15 - Two cubes have their volumes in the ratio 8: 125. Find the ratio of their surface areas.
Answer - A
Explanation
Let their edges be X and Y. Then, X3/Y3 = 8/125 (or) (X/Y)3 = (2/5)3 (or) (X/Y) = (2/5). Ratio of their surface area = 6X2/6Y2 = X2/Y2 = (X/Y)2 = 4/25, i.e. 4:25.
Q 16 - Find the volume and surface area of a sphere of radius 21 cm.
Answer - B
Explanation
Volume = (4/3)πr3 =(4/3)*(22/7)*(21)*(21)*(21) cm3 = 38808 cm3. Surface area = 4πr2 =(4*(22/7)*(21)*(21)) cm2 = 5544 cm2
Q 17 - The volume of a wall, 10 times as high as it is broad and 16 times as long as it is high, is 25.6 m3. Find the breadth of the wall.
Answer - A
Explanation
Let the breadth of the wall be X meters. Then, Height = 10X meters and Length = 160X meters. X x 10X x 160X = 25.6 ⇒ X3=25.6/1600 =2/125 ⇒X = ∛2/5 m
Q 18 - Two metallic right circular cones having their heights 4.1 cm and 4.3 cm and the radii of their bases 2.1 cm each have been melted together and recast into a sphere. Find the diameter of the sphere.
Answer - A
Explanation
Volume of sphere = Volume of 2 cones = (1/3 π x (12) x 2.2 + 1/3 π x (1)2 x 1.8) = 4/3 π Let the radius of sphere be R 4/3 π R3 = 4/3 π or R = 1cm Hence , diameter of the sphere = 2 cm
Q 19 - The diameter of garden roller is 2.8 m and it is 3 m long. The area covered by the roller in 10 revolutions is?
Answer - B
Explanation
Curved surface area of roller = (2 π R H) = 2 x π x 1.4 x 3=132/5. Area covered by the roller = 10 x (132/5) =264 m2
Q 20 - The curved surface area of a cylindrical pillar is 440 m2 and its volume is 1540 m3. Find the ratio of its diameter to its height.
Answer - A
Explanation
Curved surface area = (2 π R H) = 440 ⇒ R x H=70 ... (1) Volume = ⇒ R2H=1540 ⇒ R2 x H =490 ... (2) Solving 1 & 2 we get R=7 m H= 10 m Required ratio = 2R/H =14/10 =7/5 =7:5