Question

4
Q no.6
circle is a rno
From a solid right circular cylinder with a height 12cm
and radius of the base 5cm, a right circular cone of the
same height and the same base radius is removed. Find
the total surface area of the remaining solid. (n = 22/7)​

Answer 1

Step-by-step explanation:

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Answer 2

Question :-

From a solid right circular cylinder with a height 12 cm  and radius of the base 5 cm, a right circular cone of the  same height and the same base radius is removed. Find  the total surface area of the remaining solid. (π = 22/7)​

Given :-

Height of solid circular cylinder = 12 cm

Radius of the base = 5 cm

To Find :-

The total surface area of the remaining solid.

Analysis :-

Volume of the remaining solid = Volume of the cylinder − Volume of the cone

Whole surface area = Curved surface area of the cylinder + Area of the base the cylinder + Curved surface area of cone

Solution :-

We know that,

• h = Height
• r = Radius
• CSA = Curved Surface Area
• TSA = Total Surface Area

Given that,

Height = 12 cm

Radius of the base = 5 cm

According to the question,

$\underline{\boxed{\sf Slant \ height \ of \ the \ cone=l\sqrt{r^{2}+h^{2}} }}$

Substituting their values, we get

Slant height of the cone = $\sf \sqrt{5^{2}+(12)^{2}}$

Solving them, we get

Slant height $\implies \sf \sqrt{169} \: cm=13 \: m$

Volume of the remaining solid = Volume of the cylinder − Volume of the cone

Substituting the formula, we get

$\longrightarrow \sf \pi r^{2}h-\dfrac{1}{3} \pi r^{2} h=\dfrac{2}{3} \pi r^{2}h$

Now, substituting the values into it

$\longrightarrow \sf \bigg( \dfrac{2}{3} \times 3.14 \times 5 \times 5 \times 12 \bigg) \: cm^{2}$

Solving them,

$\implies \sf 638 \: cm^{3}$

Total surface area of the remaining solid  = Curved surface area of the cylinder + Curved surface area of the cone + Area of the upper circular face of the cylinder

$\implies \sf 2 \pi rh+ \pi rl+\pi r^{2}= \pi r(2h+l+r)$

Substituting the values, by taking the value of pi as 3.14

$\implies \sf [3.14 \times 5 \times (2 \times 12 +13+5)] \: cm^{2}$

$\implies \sf (3.14 \times 5 \times 42) \: cm^{2}$

$\implies \sf 659 \: cm^{2}$

The volume and total surface area of the remaining solid is 659 cm²

To Note :-

CSA of a cylinder of base radius r and height h = 2π × r × h

TSA  of a cylinder of base radius r and height h = 2π × r × h + area of two circular bases