Question

If r=5cm and h=12cm then find the T.S.A of cylinder and cone

Answer 1

Answer:

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Step-by-step explanation:

The total surface area of a cone  =  SA = πr^2+πr s

Where:

r = radius

s= slant height

To find the slant height consider the right triangle formed by the radius(base), the height(vertical leg) then the slant height is the hypotenuse so:

s^2=r^2+h^2

= 5^2+12^2 = 169

s=13cm

Thus:

SA=22/7(25 + 5 * 13)

= 1980/7  =  282.85 cm

= 282  6/7 cm^2 (it's a mixed fraction)

=====

Total surface area of cylinder = 2πr(r + h)

= 2 * 22/7 * 5 (5 + 12)  = 534.28

= 534  7/25 cm^2 (it's a mixed fraction)

Answer 2

Given:

• Radius of a cylinder = 5 cm

• Height of the same cylinder = 12 cm

To Find:

Total Surface Area of the Cylinder and Cone having same dimensions.

Concept:

Total Surface Area of a Cylinder = $2\pi r(h+r)$

Total Surface Area of a Cone = $\pi r l + \pi r^2$

where,

r = radius of the cylinder or cone

h = height of cylinder or cone

l = slant height of cone

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

Solution:

First calculating Total Surface Area of Cylinder.

Total Surface Area of Cylinder = $2\times\dfrac{22}{7}\times5\left(5+12\right)\:\: cm^2$

Total Surface Area of Cylinder = $2\times\dfrac{22}{7}\times5\times17\:\:cm^2$

Total Surface Area of Cylinder = 534.286 $cm^2$

Now calculating Total Surface Area of Cone.

Since , slant height is unknown. We will calculate slant height first.

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

l = $\sqrt{25+144}$ cm

l = $\sqrt{169}$

l = 13 cm

Substituting the values of r and l in the formula,

Total Surface Area of Cone= $\sqrt{\pi \times 5 \times 13+\pi \times 5^2}\:\: {cm}^2$

Total Surface Area of Cone= $\dfrac{22}{7}\left(65+25\right)\:\:{cm}^2$

Total Surface Area of Cone= 282.857 ${cm}^2$

Therefore, the answer is 534.286 $cm^2$ and 282.857 ${cm}^2$.

✨Other Formulas of

Cylinder:✨

• Lateral Surface Area= 2πrh

• Total Surface Area = 2πr(h + r)

⭐Formulas of Hollow Cylinder:⭐

Let the external radius , internal radius and height of a hollow cylinder be R , r and h respectively.

• Thickness of Hollow Cylinder = R-r

• Area of cross section = $\pi (R^2-r^2)$

• External Curved Surface Area = 2πRh

• Internal Curved Surface Area = 2πrh

• Total Surface Area = external curved surface area + internal curved surface area + area of two ends

$\:\:\:\:\:\:\:\:\: = 2πRh + 2πrh + 2π(R^2-r^2)$

$\:\:\:\:\:\:\:\:\: = 2π(Rh + rh + R^2-r^2)$

• Volume of material used = $πR^2h - πr^2h$

$\:\:\:\:\:\:\:\:\: = πh(R^2-r^2)$