Question

The radius and height of a right circula cone æe in the ratio 43 zits volume is
2156cu. Cm. find the curved surface area and the total surface ze of the core.​

Answer 1

Answer:

• 1386cm²

Given:

• Radius and height of a right circular cone in the ratio 4 : 3
• Area of right circular cone is 2156 cm²

To find :

• TSA

Solution:

• Let the radius of right circular cone be 4x
• Let the height of right circular cone be 3x

And also Given the area of right circular cone is 2156 cm²

As we know that:

• volume of cone = ⅓ πr²h

where,

• r is 4x
• h is 3x
• volume of cone is 2156

⟶ volume of cone = ⅓ πr²h

⟶ 2156 = ⅓ × 22/7 × (4x)² × 3x

⟶ 2156 = ⅓ × 22/7 × 16x² x 3x

⟶ 2156 = 22/7 × 16x² × x

⟶ 16x³ = 2156 × 7/22

⟶ x³ = 98 × 7/16

⟶ x³ = 7 × 7 × 7/2 × 2 × 2

⟶ x = 7/2

⟶ x = 3.5m

so now ,

• Radius of right circular cone = 4x = 4(3.5) = 14cm
• Height of right circular cone = 3x = 3(3.5)= 10.5 cm

Now to find the slant height:

As we know that

• slant height = (l²) = r² + h²

where,

• r is 14cm
• h is 10.5cm

⟶ (l²) = r² + h²

⟶ (l²) = (14)² + (3.5)²

⟶ (l²) = 196 + 110.25

⟶ (l²) = 306.25

⟶ l = √ 306.25

⟶ l = √ 306.25

⟶ l = 17.5 cm

Slant height is 17.5 cm

Now we have to find the curved surface area :

As we know that

• csa = πrl

● πrl

● 22/7 × 14 × 10.5

● 22 × 2 × 10.5

● 44 × 10.5

● 770 cm²

curved surfaced area of cone is 770 cm²

Now we have to find the total surface area of cone:

As we know that :

• TSA = πr² + πrl

● πr² + πrl

● 22/7 × 14² + 770

● 616 + 770

● 1386 cm²

Total surfaced area of cone is 1386 cm²

Answer 2

Answer:

Answer:

Curved surface area of cone = 770 cm²

Total Surface area of cone = 1386 cm²

Step-by-step explanation:

The radius and height of a right circular cone are in the ratio 4:3 and it's volume is 2156 cu. cm. Find the curved surface area and total surface area of the cone

Volume of a cone = (1/3)π r² h

r = Radius

h = Height

Let say radius = 4x cm

then height = 3x cm

Volume of a cone = (1/3) (22/7) (4x)² (3x)

= (22/7) (16) x³

(22/7) (16) x³ = 2156

=> x³ = (2156 * 7) / (22 * 16)

=> x³ = 98 * 7 / 16

=> x³ = 49 * 7 / 8

=> x³ = 7³/2³

=> x = 7/2

Radius = 4x = 4*7/2 = 14cm

Height = 3*7/2 = 10.5 cm

Slant Height = l cm

l² = r² + h²

=> l² = 14² + (10.5)²

=> l² = 196 + 110.25

=> l² = 306.25

=> l = 17.5 cm

Curved Surface Area = π r l

= (22/7) * 14 * 17.5

= 44 * 17.5

= 770 cm²

Curved surface area of cone = 770 cm²

Total Surface Area = π r² + π r l

= (22/7) * 14² + 770

= 616 + 770

= 1386 cm²

Total Surface area of cone = 1386 cm²

Step-by-step explanation:

Hope this answer will help you✌