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An ice-cream seller sells his ice - creams in two ways

(A) In a cone of $r = 5 cm, h = 8 cm$ with a hemispherical top.

(B) In a cup in shape of cylinder with $r = 5 cm, h = 8 cm$

He charges the same price for both but prefers to sell his ice-cream in a cone.

(a) Find the volume of the cone and the cup.

(b) Which out of the two has more capacity?
(c) By choosing a cone, which value is not being followed by the ice-cream seller?

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314 {cm}^{3}

628 {cm}^{3}

, b- cup have more capacity, c- By choosing cone the ice cream seller is being dishonese

314 {cm}^{3}

528 {cm}^{3}

, b- cup have more capacity, c- By choosing cone the ice cream seller is being dishonese

312 {cm}^{3}

228 {cm}^{3}

, b- Cone have more capacity, c- By choosing Cup the ice cream seller is being dishonese

314 {cm}^{3}

280 {cm}^{3}

, b- Cone have more capacity, c- By choosing cup the ice cream seller is being dishonese

answer is A.

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Detailed Solution

Given,
Radius of cone = 5 cm
Height of cone = 8 cm
(a) Cone volume –
Slant height of cone

l = \sqrt{r^{2} + h^{2}}

l = \sqrt{5^{2} + 8^{2}}

So, the

volume of ice cream

v_{i} = \frac{1}{3} π r^{2} h

v_{i} = \frac{1}{2} \times \frac{22}{7} \times 25 \times 8

v_{i} = 100 \times 3.14 {cm}^{3}

v_{i} = 314 {cm}^{3} .

Now, cylindrical cup Volume

= π r^{2} h

= 3.14 \times 25 \times 8

= 200 \times 3.14 {cm}^{3}

= 628 {cm}^{3}

(b) Here, the capacity of a cup is twice that of a cone.
So, the capacity of cone is more.
(c) Here, with choosing the cone the sells man of ice cream is being dishonese. Hence, solved option 1 is correct.

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