Question

17. A rectangular metal block has length 10 cm, breadth 8 cm and height 2 cm. From this block, a
cubical hole of side 2 cm is drilled out. Calculate the volume and surface area of the remaining
solid.​

Answer 1

Answer:

156 cm³, 228 cm²

Step-by-step explanation:

volume of cuboid - volume of cube

surface area of cuboid - area of square

Answer 2

Given :

• Length of rectangular metal block = 10 cm.

• Breadth of rectangular metal block = 8 cm.

• Height of rectangular metal block = 2 cm.

• Cubical hole of side 2 cm is drilled out.

To calculate :

• The volume and surface area of the remaining solid = ?

Solution :

We need to find the surface area of block = ?

$\qquad : \implies \sf S_B \ = \ 2 (lb + bh +hl)$

$\qquad : \implies \sf 2 (10 \times 8 \ + \ 8 \times 2 \ + \ 2 \times 10)$

$\quad {\underline {\boxed {\sf SA \ of \ block \ = \ 232 \ cm^2}}}$

Now,

Finding the surface area of 4 faces of cubical hole.

$\qquad : \implies \sf S_C \ = \ 4 \times (2 \times 2)$

$\quad {\underline {\boxed {\sf SA \ of \ 4 \ faces \ of \ cubical \ hole \ = \ 16 \ cm^2}}}$

Then,

Finding the area of remaining solid = ?

$\bullet \ \sf S_B \ + \ S_C \ - \ SA \ of \ 2 \ faces \ of \ cubical \ hole$

$\qquad : \implies \sf 232 \ - \ 16 \ - \ 2 (2 \times 2)$

$\qquad : \implies \sf 248 \ - \ 8$

$\quad {\underline {\boxed {\sf SA \ of \ remaining \ solid \ = \ 240 \ cm^2}}}$

Now,

To find the volume of remaining solid,

$\bullet \ \sf Volume \ of \ block \ - \ volume \ of \ cubical \ block$

$\qquad : \implies \sf 10 \times 3 \times 2 \ - \ 2 \times 2 \times 2$

$\qquad : \implies \sf 160 \ - \ 8$

$\quad \blue {\underline {\boxed {\sf Volume \ of \ remaining \ solid \ = \ 152 \ cm^3}}}$

$\therefore$ The Volume of the remaining solid is 152³.