9th Grade > Mathematics
SURFACE AREAS AND VOLUMES MCQs
:
B
Given that, the radius of the sphere is r.
Since the cricket ball fits exactly inside the cylinder tin, the height of the cylinder (h) will be equal to the diameter of the ball .
⇒h=2r
Ratio of their surface areas
=Surface area of ballSurface area of cylindrical tin
=4 π r22 π r(r+h)
=2rr+h
=2rr+2r
=23
=2:3
Hence, required ratio is 2:3
:
C
Let the radius of the old cylinder be R and that of the new cylinder be r.
Then, r=R2
Volume of old cylinder=πR2h
Volume of new cylinder=πr2h
=π×(R2)2×h
=π×R2×h4
Hence, reduction in volume
=Volume of old cylinder - volume of new cylinder
=πR2h−π×R2×h4=34πR2h
∴ Percentage reduction
=Reduction in volumeVolume of old cylinder×100
=34πR2hπR2h×100
=75%
:
C
Volume of the big iron ball will be equal to the volume of 27 small iron balls.
Let the radius of the big sphere be R cm.
Let the radius of the small sphere be
r cm = 5 cm.
⇒ 43×πR3=27×(43×πr3)
⇒R3=27r3
R=3r=3×5=15 cm.
:
B
The area of aluminium sheet = Curved surface area of flask
⇒550 m2=πrl
⇒550=227×7×l
⇒550=22l
⇒l=25 m
Now, height of flask
⇒h=√(l2−r2)
⇒h=√252−72
⇒h=24 m
Hence, the volume of conical flask
=13 πr2h
=13×227×72× 24
=1232 m3
We know that 1 m 3=1000 litres
So, volume in litres =1232000 litres
:
C
Given that,
Radius of the tube = 3.5 cm
Length of the tube = 1 m = 100 cm
Curved surface area of cylindrical tube
=2πrh
=2×227×3.5×100
=2×22×0.5×100
=2200 cm2
Hence, the required area of the aluminium sheet is 2200 cm2.
Pavan filled water in a cylindrical vessel of radius 7cm and height 14cm. Then he gently dropped a spherical ball of radius 0.7cm. By how much should the height be increased if he doesn't want water to overflow when the spherical ball is dropped into it? Give the answer in micrometres and correct up to 2 decimal places.
___
:
Water that will flow out will be equal to the volume of spherical ball dropped into the vessel.
So,
43 π r3 = π R2 H
43 × 227 × (0.7)3 = 227 × (7)2 ×H
⇒H=0.933333 cm
1 m=10−6μm
∴H=9333.33 μm
:
rh = 43
Base area = πr2=154
⇒r=7cm so h=34×7=214
⇒l=√(h2+r2)=354
⇒ So, curved surface area = πrl
⇒ 227×(7)×354=192.5 cm2
:
The sides will be x,2x,3x
Total surface area =2(x.2x+2x.3x+x.3x)
⇒2(2x2+6x2+3x2)=88
⇒22x2=88
⇒x=2
So sides are 2 cm, 4 cm and 6 cm
So volume =2×4×6=48m3
:
C
Surface area of the boiler = Curved surface area of boiler + Base area of boiler
=2πrh+πr2
=2×227×7×10+227×72
=440+154
=594 m2
Now, number of days to corrode
=Total Surface Area of tankArea corroded per day
=5943
=198 days
∴ Boiler will take 198 days to get corroded completely.
:
D
Given,
Radius (r) = 7 cm
Slant height (l) = 10 cm
Area of the aluminium sheet required
=Total surface area of the cone
= πr(l+r)
= 227×7(10+7)
= 374 cm2
Hence, the area of the aluminium sheet required is 374 cm2.