Question

② The volume of a right circular cone is 9856 cm3

.If the diameter of the base is 28cm ,find:

(i) height of the cone (ii) slant height of the cone (iii) curved surface area of the cone​

Answer 1

Answer:

height = 48 cm

slant height = 50 cm

csa = 2200cm²

Step-by-step explanation:

volume of cone = 1/3 π r² h = 9856 cm³

r = d/2 = 28/2 = 14

π = 22/7

$\frac{1}{3} \times \frac{22}{7} \times {(14)}^{2} \times h = 9856 \\ \frac{22 \times 14 \times 14 \times h}{3 \times 7} = 9856 \\ h = \frac{9856 \times 3 \times 7}{22 \times 14 \times 14} \\ h = \frac{448 \times 3}{2 \times 14} \\ h = \frac{32 \times 3}{2} \\ h = 16 \times 3 \\ h = 48$

height of cone = 48cm

slant height of cone = l

l² = r² + h²

${l}^{2} = {r}^{2} + {h}^{2} \\ {l}^{2} = {(14)}^{2} + {(48)}^{2} \\ {l}^{2} = 196 + 2304 \\ {l}^{2} = 2500 \\ l = \sqrt{2500} \\ l = 50$

slant height of cone = 50cm

CSA of cone = π r l

$csa \: of \: cone \: = \pi \: r \: l \\ = \frac{22}{7} \times 14 \times 50 \\ = 22 \times 2 \times 50 \\ = 44 \times 50 \\ = 2200 {cm}^{2}$

CSA of cone = 2200cm²

hope you get your answer