Question

A frustum of a right circular cone is of height 16cm with radii of its ends as 8cm and 20 cm. Then, the volume of the frustum is

Answer 1

Gɪᴠᴇɴ :-

• Height = 16cm.
• Radii of its ends = 8cm & 20cm.

Tᴏ Fɪɴᴅ :-

• Volume of frustum ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• volume of frustum of cone = (1/3) * π * h * (r1² + r2² + (r1 * r2)) ...

Sᴏʟᴜᴛɪᴏɴ :-

→ h = 16cm.

→ r1 = 8cm.

→ r2 = 20cm.

→ V = volume

Putting all Values in formula we get,

→ V = (1/3) * (22/7) * 16 * (8² + 20² + (8*20))

→ V = (1/3) * (22/7) * 16 * (64 + 400 + 160)

→ V = (1/3) * (22/7) * 16 * 624

→ V = (22/7) * 16 * 208

→ V = (22 * 16 * 208)/7

→ V = (73216)/7

→ V ≈ 10459.42 cm³. (Ans.)

Hence, volume of the Frustum is 10459.42 cm³.

Answer 2

${{ \huge{ \bold{ \underline{ \red{ \mathfrak{ Question:-}}}}}}}$



▪ A frustum of a right circular cone is of height 16 cm with radii of its ends as 8 cm and 20 cm . then, find the volume of the frustum.



${ \huge{ \underline{ \mathfrak{ \red{ Solution:-}}}}}$



${ \star{ \purple{ \bold{ \underline{ \: \: Given-}}}}}$



the dimensions of a right circular cone are given as follows in the question...



¤ height of the frustum ( h )= 16 cm



¤ Radii
• ( r1 ) = 8 cm


• ( r2 ) = 20 cm



${ \star{ \purple{ \bold{ \underline{ \: \: To \: find-}}}}}$



▪ Volume of frustum of the cone??



${ \star{ \purple{ \bold{ \underline{ \: \: Formula \: used}}}}}$



${ \bold{Volume \: of \: frustum \: of \: a \: cone \: (V)}}$



${ \boxed{ \bold{ \red{V = \frac{1}{3} \pi \: h( {r1}^{2} + {r2}^{2} + (r1 \times r2))}}}}$



• substituting the above given values in the formula.....



${ \bold{V= \frac{1}{3} \pi \: 16( {8}^{2} + {20}^{2} + (8 \times 20)) {cm}^{3} }}$



${ \bold{ \implies{V = \frac{1}{3} \times \frac{22}{7} \times16 \times (64 + 400 + 160) {cm}^{3} }}}$



${ \bold{ \implies{V = \frac{1}{3} \times \frac{22}{7} \times 16 \times 624 {cm}^{3} }}}$



${ \bold{ \implies{V = \frac{22}{7} \times 16 \times 208 \: {cm}^{3} }}}$



${ \boxed{ \bold{ \red{ \: V= 10459.42 \: {cm}^{3} \: }}}}$



therefore,


the volume of frustum of the cone is equal to



${ \bold{10459.42 \: {cm}^{3} }}$