Question

find the volume curved surface area and the total surface area of a cone having base radius 35 cm and height 84 CM

Answer 1

Curved surface area = 22/7*35*91=10,010
Totally surface area =22/7*35(91+35)=13,860
Volume=1/3*22/7*35*35*84=107,800

Answer 2

Given:

Radius of the cone = 35 cm

Height of the cone = 84 cm

To find:

Volume of cone, Curved surface area and Total surface area of a cone.

Formula to be used:

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

Curved surface area of cone = πrl

Total surface area of a cone = πr ( l + r )

Solution:

Step 1 of 3:

We can find the volume of cone by using the following formula,

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

Radius of the cone, r = 35 cm

Height of the cone, l = 84 cm

Volume of cone = $\frac{1}{3}$ × $\frac{22}{7}$ × 35 × 35 × 84

Volume of cone = 22 × 5 × 35 ×28

Volume of cone = 107800 cm³

Step 2 of 3:

We can find the Curved surface area of cone by using the following formula,

Curved surface area of cone = πrl

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

l = $\sqrt{84^{2} + 35^{2} }$

l = $\sqrt{7056 + 1225 }$

l = $\sqrt{8281 }$

l = 91 cm

Curved surface area of cone = $\frac{22}{7}$ × 35 ×91

Curved surface area of cone = 22 × 5 ×91

Curved surface area of cone = 10010 cm²

Step 3 of 3:

We can find the total surface area of cone by using the following formula,

Total surface area of a cone = πr ( l + r )

Total surface area of a cone = $\frac{22}{7}$ × 35 ( 91 + 35 )

Total surface area of a cone = 22 × 5 × 126

Total surface area of a cone = 13860 cm²

Final answer:

Volume of cone is 107800 cm³

Curved surface area of cone is 10010 cm²

Total surface area of a cone is 13860 cm²