Question

the ratio of the radius and height of cone is 3:4.its volume is 301.44 find its curved surface if pie=3.14

Answer 1

hello,
let the radius be 3x and height be 4x
given V=301.44cm³
we know that V=1/3πr²h
301.44=1/3×3.14×3x×3x×4x
301.44/3.14=12x³
96=12x³
x³=8
x=2cm
therefore,radius=3x=3×2=6cm   height=4x=4×2=8cm
now,
we know that CSA of cone=πrl
where l is slant height
l=√r²+h²
l=√6²+8²
l=√36+64
l=√100
l=10cm
now CSA=3.14×6×10
=18.84×10
=188.4cm²
hope this helps,if u like it please mark it as brainliest

Answer 2

$\large{\bf{\underline{\underline{GIVEN:-}}}}$

• The ratio of radius and height of cone is 3:4. In other words:

$\longrightarrow \sf \dfrac{r}{h} = \dfrac{3}{4}$

• Volume is 301.44 units³

$\large{\bf{\underline{\underline{TO \ FIND:-}}}}$

• CSA of cone.

$\large{\bf{\underline{\underline{SOLUTION:-}}}}$

Let radius be 3x and height be 4x.

$\red{\bigstar} \sf{\green{Volume \ of \ Cone = \dfrac{1}{3} \pi r^2 h }}$

$\sf \to 301.44 = \dfrac{1}{3} \times 3.14 \times (3x)^2 \times 4x$

$\sf \to 301.44 \times 3 \times \dfrac{1}{3.14} = 36x^3$

$\sf \to \dfrac{288}{36} = x^3$

$\sf \to 8= x^3$

$\to \sf x=\sqrt[3]{8}$

$\bf \to x= 2$

⊱ ──────  ✯  ────── ⊰

Now we know that:

1. Radius = 3x ⇒ 3 × 2 = 6 units.
2. Height = 4x = 4 × 2 = 8 units.

⇒ Slant height = √(r² + h²)

⇒ l = √(6² + 8²)

⇒ l = 10 units.

$\red{\bigstar} \sf{\green{CSA \ of \ Cone = \pi \times r \times l }}$

$\sf \to CSA \ of \ Cone = 3.14 \times 6 \times 10$

$\bf \to CSA = 188.4 \ units^2$

Therefore CSA is 188.4 units².

More formulae:

• Surface area of a cuboid = 2 (lb + bh + hl)
• Surface area of a cube = 6a²
• Curved surface area of a cylinder = 2πrh
• Total surface area of a cylinder = 2πr(r+h)
• Curved surface area of a cone = πrl
• Total surface area of a right circular = πrl + πr²
• Surface area of a sphere =4πr²
• Curved surface area of a hemisphere = 2πr²
• Total surface area of a hemisphere = 3πr²
• Volume of a cube = a³
• Volume of a cylinder = πr²h
• Volume of a cone = 1/3πr²h
• Total surface area of cone = πrl + πr²
• Volume of a sphere =4/3πr²
• Volume of a hemisphere = 2/3πr³