(A) Let the radius of the base be $r$ and the height be $h = 6 \, m$.The area of one circular face is $\pi r^2$. The sum of the areas of the two circu

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(A) Let the radius of the base be $r$ and the height be $h = 6 \, m$.The area of one circular face is $\pi r^2$. The sum of the areas of the two circular faces is $2 \pi r^2$.The area of the curved surface of the cylinder is $2 \pi r h$.According to the problem,$3 \times (2 \pi r^2) = 2 \times (2 \pi r h)$.Substituting $h = 6$,we get $6 \pi r^2 = 4 \pi r (6)$.Dividing both sides by $2 \pi r$ (assuming $r \neq 0$),we get $3r = 2(6)$.$3r = 12$.$r = 4 \, m$.

Competitive Quantitative Aptitude Mensuration Measurement of Volume and Surface Area

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The height of a right circular cylinder is $6 \, m$. $3$ times the sum of the areas of its two circular faces is equal to twice the area of its curved surface. The radius of the base is ...... $m$.

A
$4$
B
$2$
C
$6$
D
$1.5$

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Measurement of Volume and Surface Area

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The height of a circular cylinder is increased $6$ times and the base area is decreased to $\frac{1}{9}$ of its value. The factor by which the lateral surface area of the cylinder increases is

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The base of a prism is a right-angled triangle with $2$ sides $5 \, cm$ and $12 \, cm$. The height of the prism is $10 \, cm$. The total surface area of the prism is......$cm^2$

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There is a wooden sphere of radius $6 \sqrt{3} \text{ cm}$. The surface area of the largest possible cube cut out from the sphere will be:

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The length of an edge of a hollow cube opened at one face is $\sqrt{3}$ metres. What is the length of the largest pole that it can accommodate?

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The height of a right circular cylinder is $6 \, m$. $3$ times the sum of the areas of its two circular faces is equal to twice the area of its curved surface. The radius of the base is ...... $m$.

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$A$ brick measures $20 \, cm$ by $10 \, cm$ by $7.5 \, cm$. How many bricks will be required to construct a wall $25 \, m$ long,$2 \, m$ high,and $0.75 \, m$ thick?

The height of a circular cylinder is increased $6$ times and the base area is decreased to $\frac{1}{9}$ of its value. The factor by which the lateral surface area of the cylinder increases is

The base of a prism is a right-angled triangle with $2$ sides $5 \, cm$ and $12 \, cm$. The height of the prism is $10 \, cm$. The total surface area of the prism is......$cm^2$

There is a wooden sphere of radius $6 \sqrt{3} \text{ cm}$. The surface area of the largest possible cube cut out from the sphere will be:

The length of an edge of a hollow cube opened at one face is $\sqrt{3}$ metres. What is the length of the largest pole that it can accommodate?

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