A conical glass has a diameter of 8.4cm and height 9cm When the glass is 75% full, how many mL of juice does it contain? If the juice is poured into a cylinder of same diameter how high will it rise?

Answers 2

Step-by-step explanation:

d =8.4cm r = 4.2cm h =9cm

amount of juice contained when the glass is 75% full =

75 / 100 × full vol. of conical glass

= 3/4 × 1/3 × 22 /7 × 4.2 × 4.2 × 9

= 124.74cm³

as 1cm³ = 1 ml

hence 124.74 cm³ of juice contained when the glass is 75% full.

let the height of the juice raised in each cylinder = H cm

vol. of cylinder = vol. of juice in conical glass

22/7 × 4.2 ×4.2 ×H = 1/3 × 22/7 × 4.2 × 4.2 × 9

H = 3cm

Answer:

quantity of juice the glass holds = 124.74 ml

height of cylinder = 3 cm

Step-by-step explanation:

given, diameter of conical glass = 8.4 cm

⇒ radius = 4.2 cm, height = 9 cm

volume of cone = [tex]\frac{1}{3}[/tex]πr²h

volume of conical glass = [tex]\frac{1}{3}[/tex] × [tex]\frac{22}{7}[/tex] × 4.2² × 9

= 166.32 cm³

given, the glass is 75% filled

volume of juice = [tex]\frac{75}{100}[/tex] × 166.32 = 124.74 cm³

quantity of juice the glass holds = 124.74 ml

volume of cylinder = πr²h

given, diameter of cylinder = diameter of conical glass = 8.4 cm

⇒ radius = 4.2 cm

to find: height of the cylinder (H)

volume of cylinder = volume of cone

⇒ πr²H = [tex]\frac{1}{3}[/tex]πr²h

⇒ H = [tex]\frac{1}{3}[/tex] height of conical glass = [tex]\frac{9}{3}[/tex] = 3 cm

height of cylinder = 3 cm