Question : If the sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of its diagonal is 15 cm, then its total surface area is:
Option 1: 256 cm²
Option 2: 265 cm²
Option 3: 315 cm²
Option 4: 351 cm²

Question

Question : The sum of the length and breadth of a cuboid is 16 cm. If the height of the cuboid is one-fourth of the sum of its length and breadth, then what is the lateral surface area of the cuboid?

11 Views

Answer 1

Correct Answer: 351 cm ²

Solution : Given: The sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of its diagonal is 15 cm.
Let $l, b,$ and $h$ be the length, breadth and height of the rectangular parallelepiped.
Total surface area = $2 (l b + b h + h l)$
Length of diagonal = $\sqrt{l^{2} + b^{2} + h^{2}}$
According to the question,
$\sqrt{l^{2} + b^{2} + h^{2}} = 15$
$\Rightarrow (l^{2} + b^{2} + h^{2}) = 225$
Also, ( $l + b + h$ ) = 24
$\Rightarrow (l + b + h)^{2} = 24^{2}$
$\Rightarrow l^{2} + b^{2} + h^{2} + 2 (l b + b h + h l) = 576$
$∴ 2 (l b + b h + h l) = 576 - 225 = 351$ cm ²
Hence, the correct answer is 351 cm ² .

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Law Preparation

MBA Preparation

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Resources

Exams

Top Schools

Products & Resources

NCERT Study Material

Question : If the sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of its diagonal is 15 cm, then its total surface area is:Option 1: 256 cm2Option 2: 265 cm2Option 3: 315 cm2Option 4: 351 cm2

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC MTS

Download the Careers360 App on your Android phone

Sign In/Sign Up

Question : If the sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of its diagonal is 15 cm, then its total surface area is:
Option 1: 256 cm²
Option 2: 265 cm²
Option 3: 315 cm²
Option 4: 351 cm²