Question

From solid, cylinder whose height is 15em and
the diameter is 16cm, a conical cavity of
the same height and same diameter is hollowed
out. Find the total surface area of remaining
solid.​

Answer 1

$\rm \mapsto \green{{ \underline{given \div }}}$

solid cylinder, whose height is 15 cm.

the diameter is = 16 cm.

a conical cavity of same height and same

diameter is hollow out.

$\rm \orange{\underline{\rightarrow \: to \: find \: the \: t.s.a \: of \: remaining \: solid}}$

$\rm \to \: { \underline{solution \div }}$

Height of cylinder = Height of cone = 15 cm.

Radius of the cylinder = Radius of the cone

=> 8 cm .

slant height of the cone.

$\rm \to \: l \: = \sqrt{ {h}^{2} + {r}^{2} }$

$\rm \to \: l \: = \sqrt{(15) {}^{2} + (8) {}^{2} }$

$\rm \to \: l \: = \sqrt{225 + 64}$

$\rm \to \: l \: = \sqrt{289}$

$\rm \to \: l \: = 17 \: cm$

Total surface area of the remaining solid.

=> C.S.A of cone + C.S.A of cylinder +

=> area of the base

$\rm \to \: \pi \: rl \: + 2\pi \: rh \: + \pi \: {r}^{2} \\ \\ \rm \to \: \pi \: r(l \: + \: 2h \: + r) \\ \\ \rm \to \: 3.14 \times 8(17 + 2 \times 15 + 8) \\ \\ \rm \to \: 1381.6 \: cm {}^{2}$

Answer 2

Answer:

⭐ Question⭐

✏ From solid, cylinder whose height is 15em and the diameter is 16cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of remaining solid.

⭐ Given ⭐

✏ Solid cylinder, whose height is 15 cm.

✏ Diameter is = 16 cm.

✏ A conical cavity of same height and same diameter is hollow out.

⭐ To Find ⭐

✏ T.s.a of remaining solid.

⭐ Solution ⭐

✏ Height of cylinder = Height of cone = 15 cm.

✏Radius of the cylinder = Radius of the cone = 8 cm .

✏ Slant height of the cone.

=> l= √h²+r²

=> l= √(15)² +(8)²

=> l= √225+64

=> l= √289

=> l=17cm

✏Total surface area of the remaining solid.

Total surface area of the remaining solid.

=> C.S.A of cone + C.S.A of cylinder +Total surface area of the remaining solid.

=> C.S.A of cone + C.S.A of cylinder +=> area of the base

=>πrl+2πrh+πr²

=>πr(l+2h+r)

=>3.14×8(17+2×15+8)

=>1381.6cm²

Step-by-step explanation:

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