Question

The volume of a right circular cone is 9856cm^3, of the diameter of the base is 28cm.Find height, slant height, csan

Answer 1

$\bold{given : } \\ \\ volume \: of \: a \: cone : \\ \\ 9856 \: {cm}^{2} \\ \\ \\ \\ \bold{diameter : } \\ \\ 28 \: cm \: \\ \\ radius : \\ \\ \frac{diameter}{2} \: cm \: \\ \\ \frac{28}{2} \: cm \: \\ \\ \bold{radius \: = \: 14 \: cm \: } \\ \\ \\ \\ \bold{volume \: of \: a \: cone : } \\ \\ \bold{ \frac{1}{3} \times \pi \times {r}^{2} \times h }\\ \\ 9856 \: = \frac{1}{3} \times \frac{22}{7} \times 14 \times 14 \times h \\ \\ h = \frac{9856 \times 3 \times 7}{22 \times 14 \times 14} \\ \\ h = \frac{448 \times 3}{2 \times 14} \\ \\ \bold{height \: = \: 48 \: cm \: } \\ \\ \\ \\\bold{slant \: height : ( \: l \: )} \\ \\ \sqrt{ {r}^{2} + {h}^{2} } \\ \\ \sqrt{ {14}^{2} + {48}^{2} } \\ \\ \sqrt{196 + 2304} \\ \\ \sqrt{2500} \\ \\ 50 \: cm \: \\ \\ \bold{slant \: height \: = \: 50 \: cm \: } \: \\ \\ \\ \\ \bold{curved \: surface \: area \: of \: cone \: : } \\ \\ \pi \times r \times l \\ \\ \frac{22}{7} \times 14 \times 50 \\ \\ 22 \times 2 \times 50 \\ \\ 44 \times 50 \\ \\ 220 \: {cm}^{2} \\ \\ \bold{c.s.a. \: of \: cone \: = \: 220 \: {m}^{2} }$

Answer 2

Step-by-step explanation:

Given :-

The volume of the right circular cone

= 9856cm^3

Diameter =28 cm

Radius = Diameter/2

Radius of the cone = 14cm

Solution 1 :-

Volume of the cone = 1/3πr^2h

Put the required values in the formula ,

9856 = 1/3 * 22/7 * 14 * 14 * h

h = 9856 * 3 * 7 / 22 * 14 * 14

h = 206976 / 4312

h = 48

Hence , The height of the cone is 48cm

Solution 2 :-

Radius of the cone = 14 cm

Height of the cone = 48cm

Now ,

( l )^2 = (radius)^2 + ( height )^2

Slant height ( l )^2 = √( 14)^2 + ( 48)^2

( l )^2 = 196 + 2304

( l )^2 = 2500

l = 50 cm

Thus , The slant height of a cone is 50 cm

Solution 3 :-

Total surface area of cone

Put the required values in the formula ,

TSA of cone = 22/7 * 14 ( 50 + 14)

TSA of cone = 22 * 2 * 64

TSA of cone = 2816 cm²