Question

volume of right circular cone is 2200÷ 7 cubic cm and its Diameter is 10 cm . find the slant height also find the curved surface area of cone in terms of Pi

Answer 1

radius be 10/2 cm=5cm.let slant height be l
now 1/3 ×22/7 ×5×5×h=2200/7 or, h=(100×3)/25
or, h=12. now l^2=r^2+h^2
or,l^2=25+144
so l=13
curved surface area of cone=pi. 5×13 cm^2
=65pi cm^2 (ans)

Answer 2

The slant height is 13 cm, and the curved surface area of the cone in terms of Pi is 65π cm².

Given:

Volume of the right circular cone =  $\bf \frac{2200}{7}$ cubic cm

Diameter of the right circular cone = 10 cm

To find: The slant height and the curved surface area of the cone in terms of Pi.

Formula used:

• Volume of the right circular cone = $\bf \frac{1}{3} \pi r^2 h$
• Slant height, $\bf l^2 = r^2 + h^2$
• Curved surface area of the cone = πrl

Solution:

Step1: Find Slant height:

Let the slant height be 'l' .

Radius ,r =  10/2 cm = 5cm

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

$\bf \frac{2200}{7} = \frac{1}{3} \times \frac{22}{7} \times 5 \times 5 \times h$

$\bf 2200 \times 3 = 22 \times 25 \times h \\\\\h = \frac{2200 \times 3}{22 \times 25} \\\\h = \frac{100 \times 3}{25}$

h = 4 × 3

h = 12 cm

Slant height,  $\bf l^2 = r^2 + h^2$

$\bf l^2 = 5^2 + 12^2$

$\bf l^2 = 25 + 144$

$\bf l^2 = 169$

l = 13 cm

Slant height = 13 cm

Step2: Find the curved surface area of cone:

Curved surface area of cone = $\bf \pi \times 5 \times 13$

Curved surface area of cone = 65π cm²

Hence, the slant height is 13 cm, and the curved surface area of the cone in terms of Pi is 65π cm².

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