Question

find tsa lsa and cros section ​

Answer 1

Answer:

Area of a Hollow Cylinder:

2π ( r1 + r2)( r1 – r2 +h)

Defining Terms:

Let ‘r1‘ be the outer radius of the given cylinder and ‘r2‘ be its inner radius and ‘h‘ be its height.

‘C1‘ be the outer circumference and ‘C2‘ be the inner circumference.

L1 and L2 be the outer and inner surface areas respectively.

t be the thickness of the cylinder (r1−r2)

Area of Hollow Cylinder formulas:

The Circumference of a circle (C) is given by:

C=2πr, therefore,C1=2πr1C2=2πr2

The Lateral Surface Area (L),for a cylinder is:

L=C×h=2πrh, therefore,

L1=2πr1h, the external curved surface area

L2=2πr2h, the internal curved surface area

Thus Lateral Surface Area of a hollow cylinder = L=2πr1h+2πr2h

Cross sectional Area:

Let A be the area of a cross-section of a hollow cylinder,

A = πr2, for a circle, therefore,

A1 = πr21 for the area enclosed by r1

A2 = πr22 for the area enclosed by r2

A = A1 – A2 for the cross sectional area of hollow cylinder

A = πr21−πr22=π(r21−r22)

Total Surface Area of a Hollow Cylinder:

=2πh(r1+r2)+2π(r21–r22)

=2πh(r1+r2)+2π(r21+r22)(r21–r22)

=2π(r1+r2)(h+r1–r2)

Example: Find (in cm2) the curved surface area of a hollow cylinder with thickness 2 cm external radius 8 cm and height is 20 cm.

Solution: Let the external radius, the internal radius and the height of the hollow cylinder be r1, r2 and h respectively.

r2= 8-2 = 6 cm.

Curved surface area of a hollow cylinder = 2πr1h+2πr2h= 2πh(r1+r2)=2×227×20(8+6)=1760cm2

Step-by-step explanation:

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