Question

If the volume of right circular cone is 128 pie cm3 and its height is 6 cm. Find its,i) radius ii) total surface area

Answer 1

Step-by-step explanation:

$\text{\large\underline{\orange{Given:}}}$

• The volume of right circular cone (V) = 128$\pi$ cm³
• Height (h) = 6 cm

$\text{\large\underline{\pink{To\:find:}}}$

• (i) It's radius = ?
• (ii) TSA = ?

$\text{\large\underline{\red{Solution:}}}$

We know, $\blue{volume \: of \: cone \: = \: \frac{1}{3} \pi {r}^{2}h}$

(i) (For radius just put the values)...

$\implies$ $128\pi \: = \: \frac{1}{3} \times \: \pi \: \times \: {r}^{2} \: 6$

$\implies$ $128 \: = \: \frac{r² × 2}{3}$

$\implies$ $\frac{128}{2} \: = \: r²$

$\implies$ $\sqrt{64} \: = \: r$

$\implies$ 8 = r

$\therefore$ Radius = 8 cm

(ii) $\blue{TSA \: of \: right \: circular \: cone \: = \: \pi \: \times \: r(l \: + \: r)}$

Slant hieght (l) = rootr² + h²

==> l = root8² + 6²

==> l = root64 + 36

==> l = root100

==> l = 10

Hence, the slant hieght (l) = 10 cm.

(now put the values into the formula of TSA)...

$\implies$ TSA = $\pi$ × 8 (10 + 8)

(it's a choice to put the value of $\pi$ here, if u'll not put your ans will not go wrong)

$\implies$ TSA = 22/7 × 18

$\implies$ TSA = 452.57 cm²

$\therefore$ TSA of right circular cone is 452.57 cm² or 3168 $\pi$ cm².

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$\text{\large\underline{\green{Let's\:know\:more\:!}}}$

TSA's:

• TSA of cuboid = 2(lb + bh + hl)
• TSA of cube = 6a²
• TSA of cylinder = 2 $\pi$ r(r + h)
• TSA of hemisphere = 3 $\pi$ r²
• TSA or CSA of sphere = 4 $\pi$ r² (sphere is 3D shape who has both TSA and CSA same)

CSA's:

• CSA of cuboid = 2(l + b) × h
• CSA of cube = 4a²
• CSA of cylinder = 2 $\pi$ rh
• CSA of hemisphere = 2 $\pi$ r²

Hope it helped you dear...