KnowledgeBoat Logo

Mathematics

The total surface area of a right circular cone of slant height 13 cm is 90π cm2. Calculate :

(i) its radius in cm

(ii) its volume in cm3.

[Take π = 3.14]

Mensuration

9 Likes

Answer

(i) Given,

Total surface area = 90π

∴ πrl + πr2 = 90π

⇒ πr(l + r) = 90π

⇒ r(l + r) = 90

⇒ r(13 + r) = 90

⇒ r2 + 13r - 90 = 0

⇒ r2 + 18r - 5r - 90 = 0

⇒ r(r + 18) - 5(r + 18) = 0

⇒ (r - 5)(r + 18) = 0

⇒ (r - 5) = 0 or (r + 18) = 0

⇒ r = 5 or r = -18.

Since, radius cannot be negative.

∴ radius = 5 cm.

Hence, radius = 5 cm.

(ii) By formula,

⇒ l2 = r2 + h2

⇒ 132 = 52 + h2

⇒ h2 = 169 - 25

⇒ h2 = 144

⇒ h = 144\sqrt{144}

⇒ h = 12 cm.

Volume = 13πr2h\dfrac{1}{3}πr^2h

= 13×3.14×(5)2×12\dfrac{1}{3} \times 3.14 \times (5)^2 \times 12

= 9423\dfrac{942}{3}

= 314 cm3.

Hence, volume of circular cone = 314 cm3.

Answered By

5 Likes

Related Questions