Question

In the given figure, from a cuboidal solid metallic block of dimension 15cm×10cm×5cm, a cylindrical hole ofa diameter 7cm is drilled out. Find the surface area of the remaining block(Take [tex](\pi=\frac{22}{7})[/tex)

Answer 1

Answer:

The Surface area of the remaining block = 583 cm².

Step-by-step explanation:

SOLUTION :  

FIGURE IS IN THE ATTACHMENT

GIVEN:

Length of the cuboidal solid metallic block(l) = 15 cm.

Breadth of the cuboidal solid metallic block(b) = 10 cm.

Height of the cuboidal solid metallic block = height of the cylinder (h) =  5 cm.

Diameter of a cylindrical hole(d)= 7 cm

Radius of a cylindrical hole = d/2 = 7/2  

Surface area of a cuboid = 2(lb + bh + hl)

Surface area of a cuboid = 2(15×10 + 10×5 + 5×15)

= 2 (150 + 50 + 75) = 2 × 375 = 550 cm²

Surface area of a cuboid = 550 cm²

Curved surface Area of a cylinder = 2πrh

= 2 × (22/7) × (7/2) × 5 = 22 × 5 = 110 cm²

Curved surface Area of a cylinder = 110 cm²

Area of  2 cylindrical holes = 2(πr²)

= 2 × (22/7) × (7/2)²

= 2 × (22/7) × (7/2) × (7/2)

= 11 × 7  = 77 cm²

Area of  2 cylindrical holes = 77 cm²

Surface area of the remaining block = surface area of the cuboidal block + CSA of cylinder - Area of  2 cylindrical holes  

Surface area of the remaining block = 550 + 110 - 77  = 660 -77  = 583 cm²

Surface area of the remaining block = 583 cm².

Hence, the Surface area of the remaining block = 583 cm².

HOPE THIS WILL HELP YOU....

Answer 2

Let the length, breadth, and height of cuboidal be 15cm, 10cm and 5cm respectively.

Total surface area of solid cuboidal block

=

$2(lb + bh + lh) \\ \\ = 2(15 \times 10 + 10 \times 5 + 15 \times 5) \\ = 2(150 + 50 + 75) \\ = 2(275) \\ = 550c {m}^{2}$

Radius of the circular hole

$= r = \frac{7}{2}$

Area of two circular bases

$= \pi {r}^{2} + \pi {r}^{2} \\ = 2\pi {r}^{2} \\ = 2 \times \frac{22}{7} \times \frac{7}{2} \\ = 77c {m}^{2}$

Now,

Curved surface area of the cylinder

$2\pi \: rh \\ = 2 \times \frac{22}{7} \times \frac{7}{2} \times 5 \\ = 110c {m}^{2}$

Required Area

= Area Of cuboidal block - area of two circular bases + Area of cylinder

$</p><p>=550-77+110 \\ </p><p>=583c {m}^{2}$

Thanks!