Question

A juice seller serves his customers using a glass as shown in figure .The inner diameter of the cylindrical glass is 4.5 cm but the bottom of the glass has a hemispherical portion raised ,which reduces the capacity of the glass .If the height of the glass is 25cm ,find the apparent capacity of the glass and its actual capacity.
[take pie=3.14]
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Answer 1

Answer:

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Step-by-step explanation:

Apparent capacity of glass = Volume of cylinder

Actual capacity of the glass = Volume of cylinder - Volume of hemisphere

➢Volume of cylinder

Given inner diameter of the glass = 4.5 cm

➠So

➙Radius = r

$➙r = \frac{diameter}{2}$

$➙r = \frac{4.5}{2}$

$➙r = 2.25$

➙Height = 25 cm

➞Now

➣Volume of the cylindrical glass:-

$⇒\pi \: r {h}^{2}$

$⇒3.14 \times (2.25 {)}^{2} \times 25$

$⇒3.14 \times 2.25 \times 2.25 \times 25$

$⇒3.14 \times 5.0625 \times 25$

$⇒397.40625 {cm}^{3}$

➢Volume of the hemisphere:-

➙Radius of hemisphere = r = 2.25 cm

➣Volume of the hemisphere is

$⇒\frac{2}{3} \pi \: {r}^{3}$

$⇒\frac{2}{3} \times 3.14 \times (2.25 {)}^{3}$

$⇒\frac{2}{3} \times 3.14 \times 2.25 \times 2.25 \times 2.25$

$⇒\frac{2}{3} \times 3.14 \times 11.390625$

$⇒23.844375 \: {cm}^{3}$

➠Then

➯Apparent capacity of the glass = Volume of cylinder = 397.40625

➯Actual capacity of the glass is

➢Total volume of cylinder - volume of hemisphere

⇒397.40625 - 23.844375

⇒373.561875

➠Hence,

➣Apparent capacity = 397.40625 cm³

➢Actual capacity of the glass =

23.844375cm³

HOPE IT HELPS YOU BRO...☺❤

》》Ⱥʀɲɑѵ✯

Answer 2

Answer:

$\huge\mathfrak\green{{Answer}}$

Step-by-step explanation:

Apparent capacity of glass = Volume of cylinder

Actual capacity of the glass = Volume of cylinder - Volume of hemisphere

➢Volume of cylinder

Given inner diameter of the glass = 4.5 cm

➠So

➙Radius = r

➙r = \frac{diameter}{2}➙r=2diameter

➙r = \frac{4.5}{2}➙r=24.5

➙r = 2.25➙r=2.25

➙Height = 25 cm

➞Now

➣Volume of the cylindrical glass:-

⇒\pi \: r {h}^{2}⇒πrh2

⇒3.14 \times (2.25 {)}^{2} \times 25⇒3.14×(2.25)2×25

⇒3.14 \times 2.25 \times 2.25 \times 25⇒3.14×2.25×2.25×25

⇒3.14 × 5.0625 × 25

⇒3.14×5.0625×25

⇒397.40625cm³⇒397.40625cm3

➢Volume of the hemisphere:-

➙Radius of hemisphere = r = 2.25 cm

➣Volume of the hemisphere is

$⇒\dfrac{2}{3} \pi \:r³$

⇒32πr3

⇒\frac{2}{3} × 3.14 × (2.25)³

⇒32×3.14×(2.25)3

⇒\frac{2}{3} × 3.14 × 2.25 × 2.25 ×2.25

⇒32×3.14×2.25×2.25×2.25

⇒\frac{2}{3} × 3.14 × 11.390625

⇒32×3.14×11.390625

⇒23.844375cm³

⇒23.844375cm3

➠Then

➯Apparent capacity of the glass = Volume of cylinder = 397.40625

➯Actual capacity of the glass is

➢Total volume of cylinder - volume of hemisphere

⇒397.40625 - 23.844375

⇒373.561875

➠Hence,

➣Apparent capacity = 397.40625 cm³

➢Actual capacity of the glass =

23.844375cm³

HOPE IT HELPS YOU BRO...☺❤

》》Ⱥʀɲɑѵ✯