The dimensions of a cuboid are in the ratio o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the dimensions of the cuboid be $4x$,$3x$,and $1x$.The total surface area of a cuboid is given by the formula: $TSA = 2(lb + bh + lh)$.Substit

Vedclass · Accepted Answer

$12000$

Vedclass · Answer

(C) Let the dimensions of the cuboid be $4x$,$3x$,and $1x$.The total surface area of a cuboid is given by the formula: $TSA = 2(lb + bh + lh)$.Substituting the given values: $3800 = 2((4x)(3x) + (3x)(x) + (4x)(x))$.$3800 = 2(12x^{2} + 3x^{2} + 4x^{2})$.$3800 = 2(19x^{2})$.$3800 = 38x^{2}$.$x^{2} = 100$,which implies $x = 10 \, cm$.The dimensions are $4(10) = 40 \, cm$,$3(10) = 30 \, cm$,and $1(10) = 10 \, cm$.The volume of the cuboid is $V = l 	imes b 	imes h = 40 	imes 30 	imes 10 = 12,000 \, cm^{3}$.

The dimensions of a cuboid are in the ratio of $4: 3: 1$. If its total surface area is $3800 \, cm^{2}$,then find its volume in $cm^{3}$.

Similar Questions

The diameter of a solid sphere is $14 \, cm$. Find its surface area in $cm^2$.

The volumes of two spheres are in the ratio $64: 27$. Find the ratio of their surface areas.

State whether the following statement is True or False and justify your answer: If the radius of a cylinder is doubled and its height is halved,the volume will be doubled.

The radii of three metal spheres are $3 \,cm, 4 \,cm$ and $5 \,cm$ respectively. They are melted into a single solid sphere. Find the radius of the new solid sphere (in $cm$).

Find the total surface area of a cylinder with diameter $28 \text{ cm}$ and height $50 \text{ cm}$. (in $\text{cm}^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module