28. Calculate the volume of a solid cone of base radius 3 cm and perpendicular height 7 cm . ( Take $$ \pi=22 / 7 $$ ) $$ \begin{array}{ll} ext { (a) } 198 \mathrm{~cm}^{3} & ext { (b) } 108 \mathrm{~cm}^{3} \ ext { (c) } 68 \mathrm{~cm}^{3} \ ext { (d) } 66 \mathrm{~cm}^{3}\end{array} $$

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28. Calculate the volume of a solid cone of base radius 3 cm and perpendicular height 7 cm . ( Take $$ \pi=22 / 7 $$ ) $$ \begin{array}{ll}	ext { (a) } 198 \mathrm{~cm}^{3} & 	ext { (b) } 108 \mathrm{~cm}^{3} \ 	ext { (c) } 68 \mathrm{~cm}^{3} \ 	ext { (d) } 66 \mathrm{~cm}^{3}\end{array} $$

UpStudy AI · Accepted Answer

To calculate the volume $$ V $$ of a solid cone, we can use the formula:

$$
V = \frac{1}{3} \pi r^2 h
$$

where:
- $$ r $$ is the radius of the base,
- $$ h $$ is the height of the cone,
- $$ \pi $$ is a constant (approximately 3.14, but we will use $$ \frac{22}{7} $$ as given).

Given:
- Base radius $$ r = 3 $$ cm
- Height $$ h = 7 $$ cm
- $$ \pi = \frac{22}{7} $$

Now, substituting the values into the formula:

$$
V = \frac{1}{3} \times \frac{22}{7} \times (3)^2 \times 7
$$

Calculating $$ (3)^2 $$:

$$
(3)^2 = 9
$$

Now substituting this back into the volume formula:

$$
V = \frac{1}{3} \times \frac{22}{7} \times 9 \times 7
$$

The $$ 7 $$ in the numerator and denominator cancels out:

$$
V = \frac{1}{3} \times 22 \times 9
$$

Now calculating $$ 22 \times 9 $$:

$$
22 \times 9 = 198
$$

Now, substituting this back into the volume formula:

$$
V = \frac{198}{3}
$$

Calculating $$ \frac{198}{3} $$:

$$
\frac{198}{3} = 66
$$

Thus, the volume of the solid cone is:

$$
\boxed{66 \, \text{cm}^3}
$$

So the correct answer is (d) 66 cm³.
The volume of the cone is 66 cm³.

Calculate the volume of a solid cone of
base radius 3 cm and perpendicular
height 7 cm . ( Take )

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Calculate the volume of a solid cone of base radius 3 cm and perpendicular height 7 cm . ( Take )