Question

Q23
some
A SOLID CYLINDRICAL BLOCK OF RADIUS
12 cm AND HEIGHT 18cm is mounted
with a conical Block OF RADIUS
120cm AND HEIGHT 5 cm. THE TOTAL
LATERAL SURFACE OF THE SOLID
THUS FORMED IS​

Answer 1

Given:

A solid cylinder block of radius  12 cm and height 18cm is mounted  with a conical block of radius  12 cm and height 5 cm

To find:

The total lateral surface area of the solid thus formed

Solution:

Finding the curved surface area of the cylinderical block :

Radius, r = 12 cm

Height, h = 18 cm

∴ C.S.A. of the cylindrical block is,

= $2\pi rh$

= $2 \times \frac{22}{7} \times 12\times 18$

= $\frac{9504}{7}$

= $\bold{1357.71\:cm^2}$

Finding the curved surface area of the conical block:

Radius, r = 12 cm

Height, h = 5 cm

∴ Slant height, $l = \sqrt{r^2 + h^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \:cm$

∴ C.S.A. of the conical block is,

= $\pi r l$

= $\frac{22}{7} \times 12\times 13$

= $\frac{3432}{7}$

= $\bold{490.28\:cm^2}$

Finding the area of the bottom:

Radius, r = 12 cm

∴ Area of the circular bottom = $\pi r^2 = \frac{22}{7} \times 12^2 = \frac{22}{7} \times 144 = 452.57\:cm^2$

Finding the total lateral surface area of the solid:

∴ The total surface area of the solid formed by a cylindrical block mounted by a conical block is,

= [C.S.A. of cylindrical block] + [C.S.A. of the conical block] + [Area of the bottom]

= [1357.71 cm²] + [490.28 cm²] + [452.57 cm²]

= 2300.56 cm²

Thus, the total lateral surface area of the solid thus formed is 2300.56 cm².

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