A hemispherical bowl is filled to the brim wi | vedclass

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

Question

(C) Let the radius of the hemispherical bowl be $r$. The volume of the hemispherical bowl is $V_h = \frac{2}{3} \pi r^3$.For the cylindrical vessel,th

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(C) Let the radius of the hemispherical bowl be $r$. The volume of the hemispherical bowl is $V_h = \frac{2}{3} \pi r^3$.For the cylindrical vessel,the diameter is the same as the bowl,so its radius is also $r$. Given that the radius $r$ is $50 \%$ more than its height $h$,we have $r = h + 0.5h = 1.5h = \frac{3}{2}h$. Thus,$h = \frac{2}{3}r$.The volume of the cylindrical vessel is $V_c = \pi r^2 h = \pi r^2 (\frac{2}{3}r) = \frac{2}{3} \pi r^3$.Since the volume of the beverage transferred $(V_h)$ is equal to the volume of the cylindrical vessel $(V_c)$,the beverage fills the cylinder completely. Therefore,the volume of the beverage in the cylindrical vessel is $100 \%$ of the vessel's capacity.

Similar Questions

$A$ semicircular sheet of metal of diameter $28 \, cm$ is bent into an open conical cup. The capacity of the cup (taking $\pi = \frac{22}{7}$) is (in $cm^3$):

The base of a $10\, cm$ high solid cylinder is a semi-circle of radius $7\, cm$. Its total surface area (in $cm^2$) is (Use $\pi = \frac{22}{7}$)

The outer dimensions of a closed wooden box of $1 \text{ cm}$ thickness are $12 \text{ cm} \times 10 \text{ cm} \times 8 \text{ cm}$. Find the cost of the wood required to make the box if $1 \text{ cm}^3$ of wood costs $₹ 3.00$.

Find the weight of a hollow cylindrical lead pipe $28\, cm$ long and $0.5\, cm$ thick. Its internal diameter is $8\, cm$. (in $kg$) (Weight of $1\, cm^3$ of lead is $11.4\, g$,$\pi = \frac{22}{7}$)

$A$ cone of height $9 \, cm$ with diameter of its base $18 \, cm$ is carved out from a wooden solid sphere of radius $9 \, cm$. The percentage of the wood wasted is

Vedclass Test Series

Exam Paper Generator

Online Exam Module