Question

Find the capacity (in litres) of a conical vessel with radius 7 cm and slant height 13 cm ? Give answer with explanation step by step please. Class-9th question

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Answer 1

Answer:

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Hint: Capacity of objects implies the volume of that object.

The given question can be directly solved by using the formula of the given object.

For reference, the volume of a cone =13πr2h cubic units=13πr2⁡h cubic units .

Here, r is the base radius of the cone; h is the perpendicular height of the cone.

Assume π=227π=227 , unless stated otherwise.

Unit conversion can easily be done by the unitary method.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Complete step-by-step answer:

Step 1: Relation between base radius, slant height, and height of the cone

Let base radius of cone is denoted by r

The slant height of cone is denoted by l

And height of cone is denoted by h

Base radius and height fall perpendicular to each other, i.e., the angle between them is 90∘90∘.

Thus, a radius of length r cm, a height of length h cm, and a slant height of length l cm of the cone form a right-angled triangle.

Therefore, by applying Pythagoras theorem:

Pythagoras theorem: square of the hypotenuse is equal to the sum of the square of base and square of perpendicular.

In a right-angled triangle, the base and perpendicular are at the angle of 90∘90∘ each other and hypotenuse is the longest side.

Hypotenuse2 = Base2 + Perpendicular2Hypotenuse2⁡ = Base2 ⁡ + Perpendicular2

∵ slant height2=radius2+height2∵ slant height2=radius2+height2

⇒ l2=r2+h2⇒ l2=r2+h2

This relationship can be directly use if one of the parameter among l, r, and hl, r, and h is unknown.

Step 2: Volume calculations

Given that:

Radius, r = 7 cm

Slant height, l = 25 cm

For calculation of volume of cone base radius and height of cone should be known.

We know, l2=r2+h2 l2=r2+h2

⇒ 252=72+h2⇒ 625=49+h2⇒ h2=625−49=576⇒h=576−−−√

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