# Surface Areas and Volumes - Class 10 - Mathematics

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## Extra Questions - Surface Areas and Volumes | NCERT | Mathematics | Class 10

Two identical cubes of side $4 \mathrm{~cm}$ are placed one above the other, forming a cuboid. Find the total surface area of the cuboid thus formed.

(A) $96 \mathrm{~cm}^{2}$

(B) $100 \mathrm{~cm}^{2}$

(C) $160 \mathrm{~cm}^{2}$

(D) $180 \mathrm{~cm}^{2}$

The correct answer is **(C) $160 \mathrm{~cm}^{2}$**.

When two identical cubes, each with a side length of $4 \mathrm{~cm}$, are stacked one on top of the other, a cuboid is formed with dimensions:

Length, $l = 4 \mathrm{~cm}$

Breadth, $b = 4 \mathrm{~cm}$

Height, $h = 4 + 4 = 8 \mathrm{~cm}$

The **Total Surface Area (TSA) of a cuboid** is calculated with the formula:
$$
TSA = 2(lb + bh + hl)
$$
Plugging in the dimensions of the formed cuboid:
$$
TSA = 2(4 \times 4 + 4 \times 8 + 8 \times 4)
$$
$$
TSA = 2(16 + 32 + 32)
$$
$$
TSA = 2 \times 80
$$
$$
TSA = 160 \mathrm{~cm}^{2}
$$

Thus, the total surface area of the constructed cuboid is **$160 \mathrm{~cm}^{2}$**.

The height of a right circular cylinder is $10.5 \mathrm{~m}$. 3 times the sum of the areas of its 2 circular faces is twice the area of the curved surface. Find the volume of the cylinder.

A) $1661 \mathrm{~m}^{3}$ B) $1617 \mathrm{~m}^{3}$ C) $1579 \mathrm{~m}^{3}$ D) $1544 \mathrm{~m}^{3}$ E) $1602 \mathrm{~m}^{3}$ F) $1543 \mathrm{~m}^{3}$

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