Question

The volume of a right circular cone is 17248 cm cube .If the diameter of the base is 56cm Find its (a) height of the cone (b) slant height (c) curved surface of the cone​

Answer 1

Answer:

a ) height of the cone = 21 cm

b ) slant height = 35 cm

c) curved surface of the cone = 3080 cm³

Given:-

• volume of cone = 17248 cm³
• diameter = 56 cm
• as we know raduis is half of diameter
• radius = 28

To find:-

• height of the cone
• slant height
• curved surface of the cone

as per condition,

first we will find height of the cone

$volume \: \: of \: \: cone \: \: = \frac{1}{3} \times \pi \: \times {r}^{2} \times h \\ \\ put \: all \: the \: values \: \\ \\ \: we \: will \: take \: \: \pi \: \: = \frac{22}{7} \\ \\ 17248 = \frac{1}{3} \times \frac{22}{7} \times 28 \times 28 \times h \\ \\ \frac{17248 \times 3}{22 \times 4 \times 28} = h \: \\ \\ divide \: this \: as \: possible \: \\ \\ h \: = 21 \\ \\ now \: for \: slint \: height \\ \\ {l}^{2} = {h}^{2} + {r}^{2} \\ \\ {l}^{2} = {21}^{2} + {28}^{2} \\ \\ {l}^{2} = 441 + 748 \\ \\ {l}^{2} = 1225 \\ \\ taking \: squre \: root \: out \\ \\ l = 35 \\ \\ now \: we \: find \: \: curved \: surface \: area \: of \: cone \\ \\ curved \: surface \: area \: of \: cone = \pi \times r \times h \\ \\ curved \: surface \: area \: of \: cone = \frac{22}{7} \times 28 \times 35 \\ \\ curved \: surface \: area \: of \: cone = 88 \times 35 \\ \\ curved \: surface \: area \: of \: cone 3080 {cm}^{3}$

Answer 2

(a) height of the cone(h) = 21 cm,

(b) slant height(l) = 35 cm

(c) curved surface of the cone​ =  3080 $cm^{2}$

Step-by-step explanation:

Given:

The volume of a right circular cone = 17248 $cm^3$ and

The diameter of base(d) = 56 cm

∴ The radius of cone(r) = 28 cm

To find, (a) height of the cone(h) (b) slant height(l) (c) curved surface of the cone​ = ?

We know that,

The volume of a right circular cone $=\dfrac{1}{3} \pi r^{2}h$

⇒ $\dfrac{1}{3} \times\dfrac{22}{7} \times 28\times 28 h=17248$

⇒ $22 \times 4\times 28 h=17248\times 3$

⇒ $h=\dfrac{17248\times 3}{22 \times 4\times 28} =\dfrac{51744}{2464}$

⇒ h = 21 cm

∴ Slant height(l) $=\sqrt{r^{2}+h^{2}}$

$=\sqrt{28^{2}+21^{2}}$

$=\sqrt{784+441} =\sqrt{1225}$

= 35 cm

The curved surface of the cone​ $=\pi rl$

$=\dfrac{22}{7}\times 28 \times 35$

$=22\times 4 \times 35=88 \times 35cm^{2}$

= 3080 $cm^{2}$

Hence, (a) height of the cone(h) = 21 cm,

(b) slant height(l) = 35 cm

(c) curved surface of the cone​ =  3080 $cm^{2}$