if the area of three adjacent faces of a cuboid are X, Y, Z respectively, then the volume of cuboid is?
if the perimeter of a circle is equal to that of a squzre, then the ratio of these areas is?
two cubes have their volumes in the ratio 8:125. what is the ratio of their surface areas?
a right circular cylinder container of base radius 6cm and height 20 cm is full of ice-cream. the ice-cream is to be filled in cones of heigh 10cm and base radius 3cm, having a semi-spherical top. find the no of cones needed o empty the container?
from a solid cylinder of height 12 cm and diameter 10cm, a conical cavity of same height and same diameter is hollowed out. find the total surface area of remaining solid?
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a) Let the sides of the cuboid be a, b and c.
Given x, y and z are areas of three adjacent faces of the cuboid
Hence x=ab, y=bc, z=ca
(x)(y)(z) = (ab)(bc)(ca)
xyz= (abc)2
abc = √xyz
Thus the volume of cuboid, V= abc = √xyz
b)Let the radius of the circle be r and side of the square be a Then, according to question, 2πr=4a=>2πr4=πr2 Now, ratio of their areas, πr2(πr2)2 =πr2×4π2r2 =1411 =πr2:a2 =14:11
c)r3/R3 =8/125
(r/R)3=(2/5)3
r/R=2/5
ratio is surface area
6r2/6R2=r2/R2
=r/R*r/R
=2/5*2/5
=4/25
e)Radius of the cylinder = 6 cm
Height of the cylinder = 8 cm
Volume of the solid cylinder = πr2h
= 22/7 × 6 × 6 × 8
= 905.14 cm2
Radius of the base of the conical cavity = 6 cm
Height of the conical cavity = 8 cm
Volume of the conical cavity = 1/3 πr2h
= 1/3 × 22/7 × 6 × 6 × 8
= 301.71 cm2
Volume of the remaining solid = 905.14 - 301.71
= 603.43 cm2
Total surface area of the remaining solid = CSA of the cylinder + CSA of the conical cavity + Area of the base of the cylinder
CSA of the cylinder = 2πrh = 2π × 6 x 8 = 96 π
CSA of the conical cavity = πrl = πr√[(r)2 + (h)2]
= π x (6)2 x √[(6)2 + (8)2]
= π x (6)2 x √100
= π x 36 x 10
= 360 π
Area of the base of the cylinder = π r2 = π (6)2 = 36 π
Total surface area of the remaining solid = 96 π + 360 π + 36 π = 492 π = 492 x 3.1412 = 1545.4704 cm2
Given x, y and z are areas of three adjacent faces of the cuboid
Hence x=ab, y=bc, z=ca
(x)(y)(z) = (ab)(bc)(ca)
xyz= (abc)2
abc = √xyz
Thus the volume of cuboid, V= abc = √xyz
b)Let the radius of the circle be r and side of the square be a Then, according to question, 2πr=4a=>2πr4=πr2 Now, ratio of their areas, πr2(πr2)2 =πr2×4π2r2 =1411 =πr2:a2 =14:11
c)r3/R3 =8/125
(r/R)3=(2/5)3
r/R=2/5
ratio is surface area
6r2/6R2=r2/R2
=r/R*r/R
=2/5*2/5
=4/25
e)Radius of the cylinder = 6 cm
Height of the cylinder = 8 cm
Volume of the solid cylinder = πr2h
= 22/7 × 6 × 6 × 8
= 905.14 cm2
Radius of the base of the conical cavity = 6 cm
Height of the conical cavity = 8 cm
Volume of the conical cavity = 1/3 πr2h
= 1/3 × 22/7 × 6 × 6 × 8
= 301.71 cm2
Volume of the remaining solid = 905.14 - 301.71
= 603.43 cm2
Total surface area of the remaining solid = CSA of the cylinder + CSA of the conical cavity + Area of the base of the cylinder
CSA of the cylinder = 2πrh = 2π × 6 x 8 = 96 π
CSA of the conical cavity = πrl = πr√[(r)2 + (h)2]
= π x (6)2 x √[(6)2 + (8)2]
= π x (6)2 x √100
= π x 36 x 10
= 360 π
Area of the base of the cylinder = π r2 = π (6)2 = 36 π
Total surface area of the remaining solid = 96 π + 360 π + 36 π = 492 π = 492 x 3.1412 = 1545.4704 cm2
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