Question

plese ans both questions ​

Answer 1

Answer:

see at the summery of this chapter. you will get know about formula. r1 is upper radius and r2is bottom radius

Answer 2

Answer:

26,145.42 m² or 7592.52 cm²

Step-by-step explanation:

Depth (h) of the reservoir is  24 m and Lateral Surface area of the reservoir is 26,145.42 m².

SOLUTION :  

GIVEN :

Let ‘h’ be the height of the reservoir which is in the form of frustum of cone.

Radius of the top of the reservoir, R = 100 m

Radius of the bottom of the reservoir, r=  50 m

Volume of the reservoir = 44 × 10^7 litres

= 44 × 10^7 × 10^-3 = 44 × 10⁴ m³

[1 litres = 10^-3 m³]

Volume of the reservoir (frustum of Cone) = π/3  (R² + r² + Rr) h

= ⅓ × π (100² + 50² + 100× 50)× h

= ⅓ π (10000 + 2500 + 5000)× h

= ⅓ × 22/7  × 17500 × h

= (⅓ × 22 × 2500 × h)  

(44 × 10⁴) m³ = (⅓ × 22 × 2500 × h)  

h =  (44 × 10⁴  × 3) / (22 × 2500 )  

h = 12 × 10⁴ / 5000  

h = 12 × 10⁴ / 5 × 10³

h =  12 × 10 / 5 = 120/5 = 24 m

Depth (h) of the reservoir = 24 m

Slant height of a reservoir , l = √(R - r)² + h²

l =√(100 - 50)² + 24²

l = √50² + 576

l = √2500 + 576

l = √3076

l = 55.46 m

Lateral Surface area of the reservoir = π(R + r)l

= π(100 + 50) × 55.46

= π × 150 × 55.46

= 22/7 × 150 × 55.46

= 183,018/7

= 26,145.42 m²

Lateral Surface area of the reservoir = 26,145.42 m²

Hence, Depth (h) of the reservoir is  24 m and Lateral Surface area of the reservoir is 26,145.42 m².

OR

Let R and r be the radii of the circular ends of the frustum. (R> r)  

2R = 207.24  

R = 207.24/ (2 X 3.14)

R = 33 cm

2r = 169.56 cm  

r = 169.56 / (2 X 3.14)  

r = 27 cm

1² = h² + (R-r)²  

= 8² + (33-27)²  

l = 10 cm  

Whole surface area of the frustum

=  (R2 + r2 + (R+r)l)

= 3.14

((33)2 + (27)2 + (33+27)10)

= 3.14 (1089 +729 + 600)

= 3.14 X 2418 cm²  

= 7592.52 cm²