A hemispherical tank has an inner radius of $2.8 m .$ Its capacity is ____ $m^{3}$ .

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Concept: The capacity of hemispherical tank would be 45.99 cubic meter or 45.99L. We shall only discover the 2.8 m-diameter hemisphere's volume. This book will provide information on the hemisphere's capacity in litres. Hemisphere volume =

\frac{2}{3}

r^{3}

We are provided a hemispherical tank with an inner radius of

2.8 metre

in the question. We must determine the tanks' litre capacity. We are aware that the formula

\frac{2}{3} π r^{3}

yields the hemisphere's volume.
As a result, when we use the value of

2.8 m

for r in the formula for hemisphere volume, we get
Volume of hemisphere

= \frac{2}{3} π r^{3}

= \frac{2}{3} π {(2.8)}^{3}

= \frac{2}{3} π (2.8) (2.8) (2.8) = \frac{2}{3} π \times 21.952 = 3.14 \times 21.952 = 965.8821

= 45.9946 m^{3}

Consequently, the atmosphere's volume is

45.99 m^{3} (approx .)

We must now determine the tanks' litre capacity. We shall convert the hemispherical tank's volume into litres. To determine how many litres are contained in

45.99 m^{3},

we shall employ a unitary technique. Find the value of a single unit first, and then multiply that value by the hemisphere's volume to obtain the required value.
Since we already know that 1