Question

Find the length of the cuboid whose height and the width are 5 cm each and the volume is
300 cu cm. Also find the cost of painting its outer surface at the rate of rs 1.50.
​

Answer 1

Given :

The cuboid whose height and the width are 5 cm each and the volume is

300 cu.cm.

To find :

• Length
• Total cost of painting its outer surface at the rate of rs 1.50.

Solution :

• Height and width of cuboid = 5 cm
• Volume of cuboid = 300cm³

According to the formula of volume of cuboid

→ Length × breadth × height = 300cm³

→ l × 5 × 5 = 300

→ l × 25 = 300

→ l = 300/25

→ l = 12 cm

Now,

Total surface area of cuboid

→ 2(lb + bh + lh)

→ 2(12 × 5 + 5 × 5 + 12 × 5)

→ 2(60 + 25 + 60)

→ 2 × 145

→ 290 cm²

The cost of painting its outer surface at the rate of rs 1.50.

→ Total cost

→ 290 × 1.50

→ Rs.435

•°• Total cost of painting its outer surface = Rs.435

Focus Zone :

★ Lateral surface area of cuboid

= 2(l + b)h

★ Lateral surface area of cube = 4a²

★ Total surface area of cube = 6a²

★ Volume of cube = a³

• Where " a " is a side.

________________________________

Answer 2

Given :-

Height of cuboid = 5 cm

Width of cuboid = 5 cm

Volume = 300 cm³

Cost of painting = ₹1.50

To Find :-

Length

Total cost

Solution :-

As we know that

$\bf \: Volume = L \times B \times H$

$\sf \mapsto \: 300 =l \times 5 \times 5$

$\sf \mapsto \: 300 = 25l$

$\sf \mapsto \cancel \dfrac{300}{25} = l$

$\frak \pink{l = 12}$

Now,

For painting we will find TSA of cuboid

$\bf \: TSA = 2(lb + bh + lh)$

$\sf \mapsto \: TSA = 2(12 \times 5 + 5 \times 5 + 12 \times 5)$

$\sf \mapsto \: TSA = 2(60 + 25 + 60)$

$\sf \mapsto \: TSA = 2(145)$

$\frak \red{TSA = 290 \: c {m}^{3}}$

Now,

Finding total cost

$\sf \: Total \: cost = 290 \times 1.50$

$\sf \: Total \: cost = 435 \: rs$