Question

The total surface area of a right circular cone
of slant height 13 cm is 90 cm", find its
radius and volume.​

Answer 1

Answer:

Radius = 5 cm

Volume = ≈ 314 cm^3 OR 2200/7

Step-by-step explanation:

It should be 90$\pi$cm^2

Total surface area of right circular cone = $\pi$r(l+r)

90$\pi$ = $\pi$r(13+r)

90$\pi$/$\pi$ = r(13+r)

90 = 13r+r^2

r^2 + 13r - 90 = 0

r^2 + 18r - 5r + 90 (By splitting the middle term)

r(r + 18) - 5(r+18) (By taking common)

(r-5)(r+18)

r = 5

r = -18 ( radius cannot be negative)

So, r = 5cm

$l^{2}$ = $\sqrt{h^2+r^2}$

$13^{2}$ = $\sqrt{h^2+5^2}$

169 = $\sqrt{h^2+25}$

h = $\sqrt{169-25}$

h = $\sqrt{144}$

h = 12 cm

Volume of cone = 1/3$\pi$$r^{2}$h

= 1/3 * 3.14 * 5 * 5 * 12  

≈ 314 cm^3 OR 2200/7

Hope it help. Please mark it as the brainliest.

Answer 2

Answer:

• 314 cm²

Step-by-step explanation:

Given

• Slant height of cone = 13 cm
• T.S.A of cone = 90π cm²

To find

• Radius of cone
• Volume of cone

Solution

Let the radius of cone be r cm, then,

its total surface area will be,

• (πrl + πr²)
• πr(l + r)
• πr(13 + r) cm²

But, T.S.A = 90π cm²

∴,

• πr(13 + r) = 90π
• r(13 + r) = 90
• r² + 13r - 90 = 0
• r² + 18r - 5r - 90 = 0
• r(r + 18) - 5(r + 18) = 0
• (r + 18) (r - 5) = 0
• r = 5

∴ Radius of cone is 5 cm.

Let the height of cone be h cm,

Then, slant height,

• h² = l² - r²
• 13² - 5²
• 169 - 25
• 144
• h = √144
• h = 12

Hence, the height is 12 cm.

Now volume,

• 1/3 πr²h
• 1/3 π × 5 × 5 × 12
• 100π cm³
• 100 × 22/7
• 314 cm³

Hence, the volume of cone is 314 cm³.