Question

3. Find the volume of the largest right circular cone that can be cut out of a cube whose de
is 7 cm.​

Answer 1

ANSWER:

• volume of the cone = 89.83 cm³.

GIVEN:

• Right circular cone is cut out of a cube whose side is 7 cm.

TO FIND:

• Volume of the largest right circular cone.

FORMULA:

• Volume of cone = 1/3πr²h

EXPLANATION:

• Given that cone is cut of from the cube of side 7 cm.

• So the height of the cone will be 7 cm.

• Also diameter of the base will be equal to the side 7 cm.

h = 7 cm

r = d/2 = 7/2 cm

volume of the cone = 1/3 × 22/7 × 7/2 × 7/2 × 7

volume of cone = 1/3 × 11 × 7/2 × 7

volume of cone = (49 × 11) ÷ 6

volume of cone = (539) ÷ 6

volume of cone = 89.83 cm³.

Hence volume of the largest right circular cone that can be cut out of a cube whose side 7 cm = 89.83 cm³.

Answer 2

$\rm\huge\blue{\underline{\underline{ Question : }}}$

Find the volume of the largest right circular cone that can be cut out of a cube whose de

is 7 cm.

$\rm\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• Radius of cone with the largest volume that can be cut out from a cube of edge 7 cm = 7/2 cm.

• Height of cone = edge of cube = 7 cm.

★ Now,

• $\tt\red{ Height(h) \:_ { (Cone) } = 7 cm. }$
• $\tt\red{ Radius(r) \:_ { (Cone) } = \frac{7}{2} cm. }$

★ To find,

• Volume of cone.

★ Formula used :

$\sf\green{ Volume \: of \: cone = \frac{1}{3} \pi \:r^{2} h }$

• Substitute the values.

$\bf\:\implies \frac{1}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 7$

$\bf\:\implies \frac{11 \times 49}{6}$

$\bf\:\implies \frac{539}{6}$

$\bf\:\implies 89.83$

$\underline{\boxed{\bf{\purple{ \therefore Volume\:of\:Cone\: = 89.83 \: cm^{3}.}}}}\:\orange{\bigstar}$

⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇

★ Cone formulas :

$\rm\red{:\implies Total\:surface\:area\:of\:cone = \pi\:r(r + l) }$

$\rm\red{:\implies Curved\:surface\:area\:of\:cone = \pi\:rl }$

$\rm\red{:\implies Volume\:of\:cone = \frac{1}{3}\pi r^{2}h}$

$\rm\red{:\implies Slant\:height = l^{2} = h^{2} + r^{2}}$

⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆