Question

13
The table below shows the lateral and base areas of a right circular cone and a cylinder.
Cone Cylinder
Lateral Surface Area (sq units)
Y
Base Area (sq units)
Z
The bases of the cone and cylinder are joined to form the solid below.
What is the TOTAL surface area of the above solid?​

Answer 1

Answer:

Surface Area of a Cone

The total surface area of a cone is the sum of the area of its base and the lateral (side) surface.

The lateral surface area of a cone is the area of the lateral or side surface only.

Since a cone is closely related to a pyramid , the formulas for their surface areas are related.

Remember, the formulas for the lateral surface area of a pyramid is 12pl and the total surface area is 12pl+B .

Since the base of a cone is a circle, we substitute 2πr for p and πr2 for B where r is the radius of the base of the cylinder.

So, the formula for the lateral surface area of a right cone is L.S.A=πrl , where l is the slant height of the cone .  

Example 1:

Find the lateral surface area of a right cone if the radius is 4 cm and the slant height is 5 cm.

L.S.A=π(4)(5)=20π≈62.82  cm2

The formula for the total surface area of a right cone is T.S.A=πrl+πr2 .

Example 2:

Find the total surface area of a right cone if the radius is 6 inches and the slant height is 10 inches.

T.S.A=π(6)(10)+π(6)2=60π+36π=96π inches2≈301.59 inches2

Step-by-step explanation:

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