CUBE

Surface Area We will need to find the surface area of the top, base

and sides.

Area of the top and bottom is 2a2

Area of sides (CSA) is 4a2

Therefore the formula is: 6a2

Volume V = a 3

a

aa

a

Cuboid

Surface Area We will have to calculate the area of sides, top

and base.

Area of sides = (CSA) is 2(lh+bh) Area of top and base is 2(lb)

Therefore the formula is: 2(lb+lh+bh)

Volume v = lbh

TSA = תr(s+r)

CSA =

2πr2

Surface Area We need to find the outer surface area and the area of

the base.

Outer surface area (CSA) is 2 π r^2Area of the base is π r^2

Therefore the formula is 3 π r^2

Volume V = πr^3

Surface Area of the model = CSA of cone + CSA of cylinder = πrl + 2πrh

= π r ( l + 2h )

Surface Area of the model = CSA of the

cylinder + CSA Of the cone + Area of the

cylinder’s base= 2πrh + πrl + πr2

= πr ( 2h + l + r )

Surface Area of the model = CSA of hemisphere +

CSA of the cone = 2πr2 + πrl

= πr ( 2r + l )

Surface area of the model = CSA of the cylinder +

Surface area of the sphere –

Area of the cylinder’s base

= 2 πrh + 4 πr2 – πr2

= πr ( 2h – r ) + 4πr2

Surface area of the model = TSA of the the larger cylinder + TSA of the smaller cylinder –

Area of the smaller cylinder’s base

= 2πRH + 2πR2 + 2πrh + 2πr2 – πr2

= 2πR ( H + R ) + 2πr ( h + r )

Surface area of the model = CSA of the cylinder + CSA of

both the cones= 2πrh + 2πrl = 2πr ( h + l )

Surface area of the model = CSA of the cylinder

+ CSA of the two hemispheres

= 2πrh + 2 ( 2πr2 )= 2πrh + 4πr2

= 2πr ( h + 2r )

When two cubes are joined, they form a cuboid.

In the given model when the two cubes of side ‘a’ are joined, we get a cuboid of dimension > l = a + a b = a h = a

So the model’s surface area is 2 ( lb + bh +hl )

= 2 { ( a + a ) a + a2 + a ( a + a) }= 2 ( 2a2 + a2 + 2a2 )= 2 ( 5a2)= 10a2

Surface area of the model = CSA of the cylinder + CSA of the two hemispheres of the

same dimension

= 2πrh + 2πr2 + 2πr2

= 2πrh + 4πr2

= 2πr ( h + 2r )

Surface area of the model = TSA of the cuboid + CSA of the hemisphere - CSA of the top of the hemisphere

= 2 ( lb + hl + hb ) + 2πr2 – πr2

= 2 ( lb + hl + hb ) + πr2

Surface area of the model = TSA of the cuboid + CSA of the hemisphere - CSA of the top of the hemisphere

= 2 ( lb + hl + hb ) + 2πr2 – πr2

= 2 ( lb + hl + hb ) + πr2

Surface area of the model = CSA of the cylinder

+ CSA of the hemisphere

= 2πrh + 2πr2

= 2πr ( h + r )

• Thank you

- Dhruv Sahdev