1 Mark Question

Question 11 Mark

The Surface area of a cuboid is $1300 cm^2$. If its breadth is $10 cm$ and height is $20 cm^2$, find its length.

Answer

Let, I $\rightarrow$ Length of the cuboid
Breadth of the cuboid (b) $=10 cm$
Height of the cuboid $( h )=20 cm$
Surface area of the cuboid $(A)=1300 cm^2$
We have to find the length of the cuboid We know that,
$A=2(lb+bh+hl) 1300$
$=2(10 l+10 \times 20+20 l) 1300$
$=2(200+30 l) 1300$
$=400+601 l =\frac{1300-400}{600}$
$=\frac{900}{60}$
$=15 cm$
Length of the cuboid is 15 cm .

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Question 21 Mark

Three cubes of metal whose edges are in the ratio $3 : 4 : 5$ are melted down into a single cube whose diagonal is $12\sqrt{3}\text{cm}.$ Find the edge of three cubes.

Answer

Let the edge of the three cubes be 3x, 4x and 5x respectively. Volume of three cubes = $(3x)^3 + (4x)^3 + (5x)^3 = 216x^3 cm^3$ Let a be the edge of new cube so formed. Now, Volume of the cube = Volume of three cubes$\Rightarrow\text{a}^3=216\text{x}^3$
$\Rightarrow\text{a}=6\text{x}$
The diagonal of new cube is $12\sqrt{3}\text{cm}$$\Rightarrow\sqrt{\text{a}^2+\text{a}^2+\text{a}^2}=12\sqrt{3}$
$\Rightarrow\sqrt{3}\text{a}=12\sqrt{3}$
$\Rightarrow\text{a}=12$
$\Rightarrow\text{x}=2$
$\Rightarrow3\text{x}=6\text{cm},4\text{x}=8\text{cm}$ and $5\text{x}=10\text{cm}$

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Question 31 Mark

Find the edge of a cube whose surface area is $432m^2.$

Answer

Let, $a \rightarrow$ Edge of the cube Surface area of the cube $=6 a^2$ So, $6 a^2=432 a^2=\frac{432}{6}$
$= 72$
$\text{a}=6\sqrt{2}\text{m}$
Side of the cube is $6\sqrt{2}\text{m}.$

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Question 41 Mark

Three cubes of each sides 4cm are joined end. Find the surface area of the resulting cuboid.

Answer

Side of each cube (a) $=4 cm$
We need to find the surface area of the resulting cuboid
Dimensions of the resulting cuboid,
Length $(I)=3 a$
Breadth (b) = a
Height (h) = a
Surface area of the cuboid,
$=2(b b+b h+h l)$
$=2[(3 a) a+(a)(a)+a(3 a)]$
$=2\left(7 a^2\right)$
$=14 a^2$
$=14 \times 4^2$
$=224 cm^2$
Surface area of the cuboid is $224 cm^2$.

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Question 51 Mark

If two cubes each of sides 6cm are jioned face to face, then find the volume of the resulting cuboid.

Answer

We have,
Side of each cube (a) $=6 cm$
We need to find the volume of resulting cuboid Hence, dimensions of the resulting cuboid are, Length $( l )=2 a$
$=2 \times 6$
$=12 cm$
$\text { Breadth }(b)=a$
$=6 cm$
$\text { Height }(h)=a$
$=6 cm$
Hence, volume of the resulting cuboid,
$V=I b h$
$=12 \times 6 \times 6$
$=432 cm^3$
Hence, volume of the resulting cuboid is $432 cm^3$.

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Question 61 Mark

If the perimeter of each face of a cube is 32cm, find its lateral surface area. Note that four faces which meet the base of a cube are called its lateral faces.

Answer

Let,
a $\rightarrow$ Side of the cube
Perimeter of each face is 32 cm .
$4 a=32$
$a=8 cm$
Lateral surface area,
$=4 a^2$
$=4 \times 8^2$
$=256 cm^2$
So the lateral surface area of the cube is $256 cm^2$.

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Question 71 Mark

A cuboid has total surface area of $372 cm^2$ and its lateral surface area is $180 cm^2$, find the area of its base.

Answer

We have, Total surface area of the cuboid $(A)=372 cm^2$ Lateral surface area of the cuboid $\left(A^{\prime}\right)=180 cm^2$ Let, $a \rightarrow$ Area of the base We know that, $A = A ^{\prime}+2 a a=\frac{ A - A ^{\prime}}{2}$
$=\frac{372-180}{2}$
$=\frac{192}{2}$
$= 96\text{cm}^2$
Area of the base is $96 cm^2$.

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