Question

The radius and height of a solid right-circular cone are in the ratio of 5:12.if its volume is 314 cm^3 ,find its tsa.

Answer 1

Answer:

TSA = 282.6 cm²

Step-by-step explanation:

Given that 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.

Hence:

⇒ Radius = 5 cm.

⇒ Height = 7 cm.

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

⇒ √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)

= 282. 6 cm².

Therefore, Total surface area = 282. 6 cm².

Hope it helps!

Answer 2

Step-by-step explanation:

Given r:h = 5:12

Let r = 5x and h = 12x

Volume of cone = 314 cm3

That is (1/3)πr2h = 314

(1/3) × (3.14) × (5x)2 × 12x = 314

25x2 × 12x = 100 × 3

x3  = 1

Hence x = 1

Therefore, r = 5 cm and h = 12 cm

Slant height, l = √[r2 + h2]

                          = √[52 + 122] = √169

Therefore, slant height = 13 cm