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# The radius and height of a solid right-circular cone are in the ratio of 5 : 12. If its volume is 314 cm³ , find the total surface area.

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Proportion of  radius and height of a solid right-circular cone is given; by using relation of volume and surface area find surface area. This question was asked in 2017 cbse board exam. Question from RS Aggarwal
Chapter Mensuration
Volume and surface
Volume and Surface Area of Solid
Exercise 17A
Page number 786

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### 1 Answer

1. Given,

radius and height are in the ratio of 5:12.

Let the radius and height be 5x, 12x respectively.

It is given that Volume of cone = 314 cm³.

(1/3) × πr²h = 314

(1/3) × π × (5x)² × (12x) = 314

(1/3) × 3.14 × 25x² × 12x = 314

300x³ = 300

x³ = 1

x = 1.

∴ Radius = 5 cm. and Height = 7 cm.

We know that slant height(l) = √h² + r²

Using Pythagoras Theorem,

= √12² + 5²

=  √144 + 25

=  √169

= 13 cm.

Now,

We know that Total surface area = πr(l + r)

= 3.14 × 5 × (13 + 5)

= 3.14 × 5 × (18)

∴ Total surface area = 282. 6 cm².

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