Question

Find The Slant Height ; CSA and TSA of a Cone Whose Volume is 12936cm^3 and The Diameter of the Base is 42cm.

Answer 1

Answer:

l=35

CSA=2310 cm^2

TSA=1496 cm^2

Step-by-step explanation:

given,

volume=12936 cm^3

diameter=42 cm

radius=42/2 =21cm

volume=1/3πr^2h

12936 = 1/3×22/7×21×21×h

12936×3×7/22×21×21=h

308/11=h

28cm=h.

(l)^2=r^2+h^2

(l)^2=(21)^2+(28)^2

(l)^2= 441+784

l= √1225

l= 35cm

CSA=πrl

=22/7×21×35

=66×35

= 2310 cm^2

TSA=πr(l+r)

=22/7×21(35+21)

=22/7×21(56)

=22/7×476

=22×68

=1496cm^2.

Answer 2

Answer:

1. Slant height = 35 cm
2. Curved surface area = 2310 cm²
3. Total surface area = 3696 cm²

Step-by-step explanation:

Given that:

• Volume of a cone = 12936 cm³
• Diameter of the base = 42 cm
• Then, Radius = Diameter/2 = 42/2 = 21 cm

Formula used:

1. V = (πr²h)/3 cubic unit
2. l = √(r² + h²) unit
3. CSA = πrl sq. unit
4. TSA = πr(r + l) sq. unit

Here,

• Volume of a cone = V
• Curved surface area of a cone = CSA
• Total surface area of a cone = TSA
• Slant height of a cone = l
• Radius of the base of a cone = r
• Height of a cone = h

Finding the height of the cone:

• Volume of a cone = (πr²h)/3 cubic unit
• 12936 = (22 × 21 × 21 × h)/(7 × 3)
• 12936 = 22 × 21 × h
• h = 12936/(22 × 21)
• h = 28

∴ Height of the cone = 28 cm

To Find:

1. Slant height
2. Curved surface area
3. Total surface area

Finding the slant height:

• Slant height = √(r² + h²) unit
• Slant height = √(21² + 28²) cm
• Slant height = √(441 + 784) cm
• Slant height = √1225 cm
• Slant height = 35 cm

Finding the curved surface area:

• Curved surface area = πrl sq. unit
• Curved surface area = (22 × 21 × 35)/7 cm²
• Curved surface area = 2310 cm²

Finding the total surface area:

• Total surface area = πr(r + l) sq. unit
• Total surface area = π × 21 × (21 + 35) cm²
• Total surface area = π × 21 × 56 cm²
• Total surface area = (22 × 21 × 56)/7 cm²
• Total surface area = 3696 cm²