Question

Volume of cone is 1570 cm3. Height 15 cm. Radius?

Answer 1

Step-by-step explanation:

Right circular cone

Solve for radius

• r≈10cm
• h Height =15cm

cm

• V Volume=1570cm³

Using the formula

V=πr²h/3

Solving for

• r=3V
• πh=3·1570

π·15≈9.99746cm

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak {\purple{ \: \: SOLUTION \: \: } \mid }}}}} \:$

$\underline{ \bold{ \: Given \: : \mapsto \: }} \\ \\ \: \: \: \: \: \: \: \bold{Volume \: of \: the \: cone = 1570 \: cm {}^{3} } \\ \\ \: \: \: \: \: \: \: \text{Height \: of \: the \: cone = 15 \: cm} \\ \\ \bold{ \underline{ \: To \: \: find \: : \mapsto}} \\ \\ \: \: \: \: \: \: \: \: \text{Radius \: of \: the \: cone = ?} \\ \\ \text{Let,} \\ \\ \: \: \: \text{The \: radius \: of \: the \: cone = r} \\ \\ \underline{ \text{ \: We know that \: }} \\ \\ \boxed{\bold{Volume \: \: of \: \: cone = \frac{1}{3} \: \pi \: r {}^{2} h }}$

$\underline {\text{ \: A.T.Q. \: }} \\ \\ \: \: \: \: \: \: \: \: \: \bold{ \frac{1}{3} \: \pi \: r {}^{2} h = 1570} \\ \\ \bold{ \Rightarrow \: \frac{1}{ \cancel{3}} \times \frac{22}{7} \times r {}^{2} \times \cancel{ 15} \: {}^{5} = 1570} \\ \\ \bold{ \Rightarrow \: \frac{22 \times r {}^{2} \times 5 }{7} = 1570 } \\ \\ \bold{ \Rightarrow \: \frac{110 \: r {}^{2} }{7} = 1570 } \\ \\ \bold{ \Rightarrow \: 110 \: r {}^{2} = 10990 } \\ \\ \bold{ \Rightarrow \:r {}^{2} = \frac{10990}{110} } \\ \\ \bold{ \Rightarrow \:r {}^{2} = 99.90 } \\ \\ \bold{ \Rightarrow \:r = \sqrt{99.90} } \\ \\ \bold{ \therefore \: r = 9.99 \: \: (approx)}</p><p></p><p></p><p></p><p></p><p> </p><p>$

$\mathsf{ \therefore \: Radius \: \: of \: \: the \: \: cone \: \: is \: \: \underline{ \: 9.99 cm \: }.</p><p>}$