Question

Question numbers 1 to 8 cany 1 mark each:
1. Two cubes each with 6cm edge are joined end to end. The surface area of the resulting cuboid is
(a) 460cm?
(b) 360cm
(c) 560cm
(d) 260cm
2. The radil of the circular ends of a bucket of height 40 cm are 24cm and 15cm. The slant height (in cm) of the
bucket is
(b) 49
(a) 51
CA​

Answer 1

(1) According to the Question

When two cube with edges are joined end to end . It form new shape Cuboid. So the dimension in this case are

• Length ,l = 6+6 = 12 cm
• Breadth ,b = 6 cm (remain same)
• Height, h = 6 cm (remain same)

So we have to calculate the surface area of Cuboid(S).

• Surface Area = 2(lb+bh+lh)

Substitute the value we get

$:\implies$ Surface Area = 2(12×6+6×6+12×6)

$:\implies$ Surface Area = 2(72 +36 +72)

$:\implies$ Surface Area = 2(180)

$:\implies$ Surface Area = 360 cm²

• Hence, the surface area of the resulting cuboid is 360cm². Required Option is (b) 360cm².

_______________________________

(2)

Now, we have to calculate the slant height .

• height ,h = 40 cm
• radius ,R = 24 cm
• radius ,r = 15 cm.

• Slant height, l² = h² + (R -r)²

Substitute the value we get

$\longrightarrow$ l² = 40² + (24-15)²

$\longrightarrow$ l² = 1600 + (9)²

$\longrightarrow$ l² = 1600 + 81

$\longrightarrow$ l² = 1681

$\longrightarrow$ l = √1681

$\longrightarrow$ l = 41

• Hence , the slant height is 41 cm .

Answer 2

1. Two cubes each with 6cm edge are joined end to end. The surface area of the resulting cuboid is

(a) 460cm

(b) 360cm

(c) 560cm

(d) 260cm

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Given:-

• Edge of each cube = 6cm

To Find:-

• Surface Area of Cuboid formed

Formula used:-

• ${\boxed{TSA\: of\: Cuboid\: = 2(lb + bh + hl)}}$

Solution:-

When the two cubes are joined end to end then,

• Length of Cuboid = 6 + 6 = 12 cm

• Breadth of Cuboid = 6 cm

• Height of Cuboid = 6 cm

Putting values in Formula,

$\implies\:TSA\: = 2(lb + bh + hl)$

$\implies\:TSA\: = 2(12 \times 6+ 6 \times 6 + 6 \times 12)$

$\implies\:TSA\: = 2(72+ 36 + 72)$

$\implies\:TSA\: = 2 \times 180$

$\implies\:TSA\: = 360 cm^2$

Hence, The Surface Area of Cuboid formed is 360 cm².

[Option (b) is correct]

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2. The radii of the circular ends of a bucket of height 40 cm are 24cm and 15cm. The slant height (in cm) of the bucket is

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Given:-

• Height (h) = 40 cm

• Radius (R) = 24 cm

• radius (r) = 15 cm

To Find:-

• Slant Height of Bucket

Formula used:-

• ${\boxed{l^2= h^2 + (R -r)^2}}$

Solution:-

$\implies\:l^2= h^2 + (R -r)^2$

Putting the values,

$\implies\:l^2= 40^2 + (24 -15)^2$

$\implies\:l^2= 1600 + 9^2$

$\implies\:l^2= 1600+ 81$

$\implies\:l^2= 1681$

$\implies\:l= \sqrt{1681}$

${\boxed{\implies\:l=41cm}}$

Hence, The slant Height of Bucket is 41 cm.

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