Question

Q1. Box A measures 10 cm by 6 cm by 4 cm and Box B measures 6 cm by 6 cm
By 7 cm. Which has greater volume?
(a) Box Á
(b) Box B
(c) Both have the same volume
(d) Can't compare​

Answer 1

Step-by-step explanation:

GIVEN

In this question, we are given two boxes A and B and their dimensions are given

Box A : 10cm × 6cm × 4cm

Box B : 6cm × 6cm × 7cm

TO FIND

We need to find the volumes of the two boxes and see which one has greater volume

PROCEDURE

Volume of a cuboid is given by the formula

Volume = length × breadth × height

Box A : Volume = 10 × 6 × 4 = 240 cm^3

Box B : Volume = 6 × 6 × 7 = 252 cm^3

Therefore Box B has greater volume

Therefore, The answer to this question is

==> (b) Box B has greater volume

Answer 2

Given Question :-

Box A measures 10 cm by 6 cm by 4 cm and Box B measures 6 cm by 6 cm by 7 cm. Which has greater volume?

(a) Box Á

(b) Box B

(c) Both have the same volume

(d) Can't compare

$\large\underline\purple{\bold{Solution :- }}$

• Dimensions of Box A :-

$\begin{gathered}\begin{gathered}\bf \: dimensions \: are - \begin{cases} &\sf{Length = 10 \: cm} \\ &\sf{Breadth = 6 \: cm}\\ &\sf{Height = 4 \: cm} \end{cases}\end{gathered}\end{gathered}$

We know,

• Volume of Box A is given by

$\rm :\longmapsto\:Volume_{(Box \: A)} = Length \times Breadth \times Height$

$\rm :\longmapsto\:Volume_{(Box \: A)} = 10 \times 6 \times 4$

$\rm :\longmapsto\: \boxed{ \pink{ \bf \: Volume_{(Box \: A)} = 240 \: {cm}^{3} }}$

Now,

• Dimensions of Box B :-

$\begin{gathered}\begin{gathered}\bf \: dimensions \: are - \begin{cases} &\sf{Length = 6 \: cm} \\ &\sf{Breadth = 6 \: cm}\\ &\sf{Height = 7 \: cm} \end{cases}\end{gathered}\end{gathered}$

So,

• Volume of Box B is given by

$\rm :\longmapsto\:Volume_{(Box \: B)} = Length \times Breadth \times Height$

$\rm :\longmapsto\:Volume_{(Box \: B)} = 6 \times 6 \times 7$

$\rm :\longmapsto\: \boxed{ \pink{ \bf \: Volume_{(Box \: B)} = 252 \: {cm}^{3} }}$

Hence,

• We conclude,

$\rm :\longmapsto\: \boxed{ \pink{ \bf \: Volume_{(Box \: B)} > Volume_{(BoxA)} }}$

$\large{\boxed{\boxed{\bf{Option \: (b) \: is \: correct}}}}$

Additional Information

Additional InformationCube: 

• A cube is a three-dimensional shape which is defined XYZ plane. It has six faces, eight vertices and twelve edges. All the faces of the cube are in square shape and have equal dimensions.

Cuboid: 

• A cuboid is also a polyhedron having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel. But not all the faces of a cuboid are equal in dimensions.

Formula's of Cube :-

Total Surface Area = 6(side)²

Curved Surface Area = 4(side)²

Volume of Cube = (side)³

Diagonal of a cube = √3(side)

Perimeter of cube = 12 x side

Formula's of Cuboid

Total Surface area = 2 (Length x Breadth + breadth x height + Length x height)

Curved Surface area = 2 height(length + breadth)

Volume of the cuboid = (length × breadth × height)

lDiagonal of the cuboid =√(l² + b² + h²)

Perimeter of cuboid = 4 (length + breadth + height)