Question

please answer this question ​

Answer 1

Answer:

Radius and height of a right circular cone are in the ratio of 5:12. Let the radius and height be 5x, 12x respectively. Volume of cone = 314 cm3. (given) We know, Volume of cone = 1/3 πr2h 1/3 πr2 h = 314 1/3 x 22/7 x (5x)2 x 12x = 314 300 x3 = 300 or x = 1 This implies, Radius = 5 cm and Height = 7 cm Slant height(l) = √(h2 + r2) √122 + 52 l = √144 + 25 l = √169 or l = 13 cm. We know, Total surface area = πr(l + r) = 22/7 x 5 (13+5) = 282.6 cm2the-radius-and-height-of-right-circular-cone-are-in-the-ratio-12-if-its-volume-is-314-cubic-cm

Answer 2

Given:-

• The object is a right circular cone.
• Radius : height = 5 :12
• Volume = 314 cm³

To find:-

• Total surface area.

Answer:-

Since radius : height = 5 : 12, let the radius be $5x$ cm and the height be $12x$cm.

We know that, for a right circular cone,

$V = \dfrac{1}{3}\pi r^2h$

where,

• $V$ is volume.
• $r$ is radius.
• $h$ is height.

Putting the values given in the question,

$314 = \dfrac{1}{3} (3.14) {(5x)}^{2} 12x$

$\longrightarrow \: \dfrac{314}{3.14} = {(5x)}^{2} 4x$

$\longrightarrow \: 100 = 25 {x}^{2} \times 4x$

$\longrightarrow \: 100 = 100 {x}^{3}$

$\longrightarrow \: {x}^{3} = 1$

$\longrightarrow \: x = 1$

Hence,

• Radius = $5x\:cm=(5\times1)\:cm=5\:cm$
• Height = $12x\:cm=(12\times1)\:cm=12\:cm$

We know that, for a right circular cone,

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

where,

• $l$ is slant height
• $r$ is radius
• $h$ is height

Putting the values given,

$l = \sqrt{(5\:cm)^2 + (12\:cm)^2}$

$\longrightarrow l = \sqrt{(25 + 144)\: cm^2}$

$\longrightarrow l = \sqrt{169\:cm^2}$

$\longrightarrow l = 13\:cm$

We know that, for a right circular cone,

$TSA = \pi r (l + r)$

where,

• $TSA$ is total surface area
• $r$ is radius
• $l$ is slant height

Putting the values given,

$\longrightarrow TSA = 3.14 \times (5 \:cm)\times (13 + 5)\:cm$

$\longrightarrow TSA = 3.14 \times 5 \times 18\:cm^2$

$\longrightarrow \underline{ \underline{TSA = 282.6 \: {cm}^{2} }}$