Question

a cup is in the shape of frustum of a cone of height 6 cm.The radii of its two circular bases are 2 cm and 1 cm then the maximum water that be stored in the glass is​

Answer 1

Given:

A cup is in the shape of a frustum of a cone of height 6 cm.The radii of its two circular bases are 2 cm and 1 cm then the maximum water that is stored in the glass is​?

To find:

The maximum water that is stored in the glass

Solution:

The dimensions of the cup in the shape of a frustum of a cone:

The height, h = 6 cm

The radius of the upper base, R = 2 cm

The radius of the lower base, r = 1 cm

We know,

$\boxed{\bold{Volume\:of\:a\:frustum = \frac{1}{3} \times \pi\times h \times [R^2 + Rr + r^2]}}$

Now,

The maximum quantity of water that can be stored in the glass is,

= Volume of the frustum

= $\frac{1}{3} \times \frac{22}{7} \times 6 \times [2^2 + (2\times 1) + 1^2]}}$

= $\frac{22}{7} \times 2 \times [4 + 2 +1]}}$

= $\frac{22}{7} \times 2 \times 7$

= $22\times 2$

= $44\:cm^3$

$\boxed{\bold{1 \:cm^3 = 1 \:ml}}$

= $\bold{44\:ml}$

Thus, the maximum water that can be stored in the glass is​ → 44 ml.

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