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The curved surface area and the volume of a pillar are 264m^{2} and 396m^{3}. What is the height of the pillar?
Curved surface area of pillar = 264
⇒ 2πrh = 264
Volume of pillar = 396
⇒ πr^{2}h = 396
∴
∴ 2πrh = 264
Now
The volume of a cone is 1232 cm^{3} and the diameter of its base is 14cm. What is its slant height?
The volume of the cone = 1232
⇒ 1/3 πr^{2}h = 1232
= 24 cm
Slant height = l
The radius of a wire is decreased to one third. If volume remains the same, the length will become how many times?
Let radius be r and height be h.
New radius be r/3 and height H.
∴
Length will become 9 times.
The volume of a cube is 512 cm^{3}. What is its surface area?
Volume of the cube = 512
⇒ a^{3} = 512 = 8^{3}
⇒ a = 8
∴ Total surface area = 6a^{2} = 6 × 8^{2}
= 6 × 64 = 384 cm^{2}
A solid metallic cylinder of base radius 3cm and height 5cm is melted to make a solid cone of height 1cm and base radius 1mm. What is the number of cones?
Number of cones
= 3 × 3 × 3 × 5 × 10 × 10
= 135 × 100
= 13500
A metallic sphere of radius 10.5cm is melted and then recast into small cones each of radius 3.5cm and length 3cm. What is the number of such cones?
No. of cones
= 3 × 21 × 2 = 126
A cone and a hemisphere have equal bases and equal volumes. What is the ratio of their heights?
Cone and hemisphere have equal base means equal radii, of R cm,
Height of the cone be H cm
Height of hemisphere = R cm
Volume of cone = volume of hemisphere
H/R = 2/1
How many lead shots each 0.3 cm in diameter can be made from a cuboid of dimension 18cm × 22cm × 6cm?
No. of lead shots
= 168000
The diameter of a roller 1m long is 84 cm. If it takes 200 complete revolutions to level ground, what is the area of the ground?
Radius of roller = 84/2 = 42cm
h = 100cm
Area covered by the roller in 200
Revolutions = 200 × 2πrh
= 4 × 22 × 6
= 88 × 6 = 528 m^{2}
The curved surface area of a cylindrical pillar is 264 m^{2} and its volume is 924 m^{3}. What is the height of the pillar?
Here 2πrh = 264 m^{2}
and πr^{2}h = 924 m^{3}
∴
∴ Putting r = 7
2πrh = 264
then
A small indoor greenhouse is made entirely of glass panes including a base held together with tape. How much tape is needed for all the 12 edges?
Length of the tape = 4 (l + b + h)
= 4 (30 + 25 + 25)
= 4 × 80 = 320 cm.
How many 3 meter cubes can be cut from a cuboid measuring 18 m × 12 m × 9 m?
Edge of each cube = 3 m
Volume of each cube = (3)^{3} = 27 m^{3}
Volume of the cuboid = 18 × 12 × 9 = 1944 m^{3}
Therefore, number of cubes = 1944/27 = 72
A rectangular reservoir is 120 m long and 75 m wide. At what speed per hour must water flow into it through a square pipe of 20 cm wide so that the water rises by 2.4 m in 18 hours?
Volume of the water accumulated the reservoir 18 hours = (120 × 75 × 2.4) m^{3}
Let speed of water = v km/hour.
The width of cuboid = b = 20/100 = 1/5 m
Height = h = 20/100 = 1/5 m
Length of water cuboid formed in 18 hours
= 18 v km = 18 × 1000 v m
= 18000 v m
Volume of the water accumulated in reservoir in 18 hours
⇒ 720 v = 120 × 75 × 2.4
The thickness of a hollow wooden cylinder is 2cm. It is 35cm long and its inner radius is 12cm. What is the volume of the wood required to make the cylinder if it is open at either end?
Let r be the inner radius of the cylinder
r = 12cm
Outer radius = R = 12 + 2 = 14cm
h = 35cm
Volume of wood = π (R^{2} – r^{2}) h
A solid cylinder has a total surface area of 462 m^{2}. Its curved surface area is onethird of the total surface area. What is the volume of the cylinder?
Curved surface area
= 1/3 × total surface area
= 1/3 × 462 = 154
⇒ 2πrh = 154 …(1)
Total surface area = 462
⇒ 2πrh + 2πr^{2} = 462
⇒ 154 + 2πr^{2} = 462
⇒ 2πr^{2} = 308
Putting this value in (i), we get
2πrh = 154
∴ Volume of cylinder
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