Question

The volume of a right circular cone is 9856 cm². If the diameter of the base is 28 cm. Find the

a)height of the cone
b) slant height of the cone
c)curved surface area of the cone

Answer 1

diameter=28 cm
radius=diameter/2
radius=14 cm
The volume of a right circular cone is 9856 cm²
The volume of a right circular cone=1/3*п*r²h
1/3*22/7*14*14*h= 9856
22*28*h=9856*3
h=29568/22*28
h=29568/616
h=48cm
next, slant height (l)
l=√h²+r²
l=√48²+14²
l=√2304+196
l=√2500
l=50cm
then next, CSA of cone = (пrl)
CSA=22/7*14*50
=15400/7
CSA of cone= 2200 cm²

Answer 2

Answer:

Firstly, we will find the height of the cone :

$\\ \sf \: Radius = \frac{28}{2} \: cm = 14 \: cm$

Let the height of the cone be 'h'.

$\\ \sf \: Volume = 9856 \: \: {cm}^{3} \\ \\ \\ \implies \sf \: \frac{1}{3} \: \pi {r}^{2} h = 9856 \: \: {cm}^{3} \\ \\ \\ \implies \sf \: \frac{1}{3} \times \frac{22}{7} \times 14 \times 14 \times h = 9856 \\ \\ \\ \implies \sf \: 48 \: \: {cm}^{3} \\ \\ \\ \implies \sf \blue{h = 48 \: \: {cm}^{3} }$

Therefore, the height of the cone is 48 cm³.

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$\\ \sf \: Slant \: \: height \: \: of \: \: cone \: \: (l) = \sqrt{ {r}^{2} + {h}^{2} } \\ \\ \\ \implies \sf \: \sqrt{ {14}^{2} + {48}^{2} } \\ \\ \\ \implies \sf \: \sqrt{196 + 2304} \: \: cm \\ \\ \\ \implies \sf \red{50 \: \: cm}$

Therefore, the slant height of the cone is 50 cm.

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$\\ \sf \: Csa \: \: of \: \: cone = \pi \: rl \\ \\ \\ \implies \sf \: \frac{22}{7} \times 14 \times 50 \\ \\ \\ \implies \sf \: 22 \times 100 \\ \\ \\ \implies \sf \green{2200 \: \: {cm}^{2} }$

Therefore, curved surface area of the cone is 2200 cm².