5 Marks Questions

Question 15 Marks

For the cuboid shown:

$i.\ $What is the base of this cuboid?
$ii.\ $What are the lateral faces of this cuboid?
$iii.\ $Name one pair of opposite faces. How many pairs of opposite faces are there. Name them.
$iv.\ $Name all the faces of this cuboid which have $X$ as a vertex. Also, name those which have $VW$ as a side.
$v.\ $Name the edges of this cuboid which meet at the vertex $P.$ Also name those faces which meet at this vertex.

Answer

$i.\ \text{UVWX}$ is the base of a cuboid.
$ii.\ $The lateral faces for the base $\text{UVWX}$ are $\text{UXSP, QVWR, PQVU}$ and $\text{SXWR.}$
$iii.\ $Any one pair of opposite faces among the lateral faces of the base are $\text{PQVU}$ and $\text{SXWR}$ or $\text{UXSP}$ and $\text{QVWR.}$
There are two pairs of opposite faces among the lateral faces of the base of the cuboid.
$iv.\ $The faces, which have one of the vertex as $X,$ are $\text{UVWX, UXSP}$ and $\text{SXWR.}$ The faces, which have $\text{VW}$ as side, are $\text{QVWR}$ and $\text{UVWX.]}$
$v.\ $Edges which meet at $P$ are $\text{UP, SP,}$ and $\text{PQ.}$ Faces which meet at vertex $P$ are $\text{PQRS, UPSX,}$ and $\text{PQVU.}$

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Question 25 Marks

The dimensions of a cuboid with vertices $\text{A, B, C, D, E, F, G}$ and $H$ are as shown:

$i.\ $Which edges are of length $4\ cm?$ Which edges are of length $5\ cm?$
$ii.\ $Which faces have area equal to $20\ cm^2$?
$iii.\ $Which faces have the largest area$?$ What is this largest area$?$
$iv.\ $Which faces have a diagonal equal to $5\ cm?$
$v.\ $What is the area of the base of this cuboid$?$
$vi.\ $Do all the lateral faces have the same area$?$

Answer

$i.\ $The edges of $4\ cm$ length are $AD, EH, BC,$ and $FG. $ The edges of 5\ cm length are $AB, EF, CD$ and $GH.$
$ii.\ $The faces having dimensions of $5\ cm \times 4\ cm$ would have an area of $20\ cm^2$. and such faces are $\text{ABCD}$ and $EFGH.$
$iii.\ \text{ ABCD}$ and $\text{EFGH}$ have the largest area of $20\ cm^2$. There are three pairs of opposite faces of equal area. The area of opposite faces are: $3 \times 4\ cm^2, 4 \times 5\ cm^2$, and $3 \times 5\ cm^2$. and among these, $4 \times 5\ cm^2$ is the largest.
$iv.\ $The faces having sides of $3\ cm$ and $4\ cm$ respectively would have the diagonal of $5\ cm.$ (As hypotenuse of a right- angles triangle is: $3^2+ 4^2= 5^2)$. Therefore, the faces $\text{ADHE}$ and $\text{BCGF}$ have the diagonal of $5\ cm.$
$v.\ $base has $q$ dimension of $4\ cm \times 5\ cm,$ so area of abase is: $4 \times 5 = 20\ cm^2$.
$vi.\ $No, all lateral faces do not have the same area. The two lateral faces have an area of $3 \times 5 = 15\ cm^2$ and rest of the two lateral faces have an area of $3 \times 4 = 12\ cm^2$.

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