Question

The area of the base of a right circular cone is 78cm². if its height is 3 cm, then its volume will be equal to --
(A). 78cm²
(B). 224cm²
(C). 26cm²
(D). None of these​

Answer 1

The answer is (A).78cm2
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Answer 2

Answer :-

Option A.)  78 $cm^{3}$ is the correct answer.

Given :-

Measurements of right circular cone :

Area of the base = 78 $cm^{2}$

Height = 3 cm

Formula to be used :-

Area of the base = $\pi\times radius^{2}$

Volume of right circular cone = $\frac{1}{3} \times \pi \times radius^{2} \times height$

Solution :-

Area of the base = $\pi\times radius^{2}$

$=> 78\:cm^{2} =\frac{22}{7} \times radius^{2} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:[Taking\:\:\pi \:\:as\:\:\frac{22}{7} ]$

$=> \:\: \frac{78\:cm^{2}\times 7 }{22} = radius^{2} \\ \\ => \:\:3.54 \:cm^{2}\times 7 = radius^{2} \\ \\=> \:\: 24.81 \:cm^{2} = radius^{2}$

Now,

$Volume\:\:of\:\: right\:\: circular\:\: cone =\frac{1}{3} \times \pi \times radius^{2} \times height \\ \\ = \frac{1}{ 3} \times \frac{22}{7} \times 24.81 \:cm^{2} \times 3\:cm\\\\= 22\: \times 3.54\:cm^{3} \\\\=77.97\:cm^{3} \\ \\ =78 \:cm^{3} \:\:\:\:\:\:\:\:\:\:\:\:\:\:[After Round-Off]$

The volume of the right circular cone is 78 $cm^{3}$.