(D) Height $(h)$ of the cylindrical part $= 8 \, cm$.Radius $(r_{2})$ of the cylindrical part $= \frac{2}{2} = 1 \, cm$.Radius $(r_{1})$ of the spheri

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(D) Height $(h)$ of the cylindrical part $= 8 \, cm$.Radius $(r_{2})$ of the cylindrical part $= \frac{2}{2} = 1 \, cm$.Radius $(r_{1})$ of the spherical part $= \frac{8.5}{2} = 4.25 \, cm$.Volume of the vessel $=$ Volume of the sphere $+$ Volume of the cylinder.Volume $= \frac{4}{3} \pi r_{1}^{3} + \pi r_{2}^{2} h$.Volume $= \frac{4}{3} \times 3.14 \times (4.25)^{3} + 3.14 \times (1)^{2} \times 8$.Volume $= \frac{4}{3} \times 3.14 \times 76.765625 + 3.14 \times 8$.Volume $= 321.392 + 25.12 = 346.512 \, cm^{3}$.Since the calculated volume is $346.512 \, cm^{3}$,the child's measurement of $345 \, cm^{3}$ is incorrect.

Class 10 Mathematics Surface Areas and Volumes Textbook - Surface Areas and Volumes

Medium

$A$ spherical glass vessel has a cylindrical neck $8 \, cm$ long and $2 \, cm$ in diameter. The diameter of the spherical part is $8.5 \, cm$. By measuring the amount of water it holds,a child finds its volume to be $345 \, cm^{3}$. Check whether she is correct,taking the above as the inside measurements,and $\pi = 3.14$. (in $, cm^{3}$)

A
$330.25$
B
$325.12$
C
$760.768$
D
$346.51$

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Surface Areas and Volumes

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Textbook - Surface Areas and Volumes

$A$ metallic sphere of radius $4.2 \, cm$ is melted and recast into the shape of a cylinder of radius $6 \, cm$. Find the height of the cylinder. (in $cm$) [Take $\pi = \frac{22}{7}$]

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The radii of the ends of a frustum of a cone $45\, cm$ high are $28\, cm$ and $7\, cm$ (see figure). Find its volume,the curved surface area,and the total surface area (Take $\pi=\frac{22}{7}$).

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$A$ cistern,internally measuring $150 \,cm \times 120 \,cm \times 110 \,cm$,has $129600 \,cm^3$ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water,each brick being $22.5 \,cm \times 7.5 \,cm \times 6.5 \,cm$?

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The decorative block shown in the figure is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge $5 \, cm$,and the hemisphere fixed on the top has a diameter of $4.2 \, cm$. Find the total surface area of the block. (in $cm^2$) (Take $\pi = \frac{22}{7}$)

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$A$ farmer connects a pipe of internal diameter $20 \,cm$ from a canal into a cylindrical tank in her field,which is $10 \,m$ in diameter and $2 \,m$ deep. If water flows through the pipe at the rate of $3 \,km/h$,in how much time will the tank be filled? (in $minutes$) [Take $\pi = \frac{22}{7}$]

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$A$ metallic sphere of radius $4.2 \, cm$ is melted and recast into the shape of a cylinder of radius $6 \, cm$. Find the height of the cylinder. (in $cm$) [Take $\pi = \frac{22}{7}$]

The radii of the ends of a frustum of a cone $45\, cm$ high are $28\, cm$ and $7\, cm$ (see figure). Find its volume,the curved surface area,and the total surface area (Take $\pi=\frac{22}{7}$).

The decorative block shown in the figure is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge $5 \, cm$,and the hemisphere fixed on the top has a diameter of $4.2 \, cm$. Find the total surface area of the block. (in $cm^2$) (Take $\pi = \frac{22}{7}$)

$A$ farmer connects a pipe of internal diameter $20 \,cm$ from a canal into a cylindrical tank in her field,which is $10 \,m$ in diameter and $2 \,m$ deep. If water flows through the pipe at the rate of $3 \,km/h$,in how much time will the tank be filled? (in $minutes$) [Take $\pi = \frac{22}{7}$]

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