(D) The penholder is a cylinder with a base,so its surface area is the sum of the curved surface area and the area of the circular base.Radius $(r) =

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(D) The penholder is a cylinder with a base,so its surface area is the sum of the curved surface area and the area of the circular base.Radius $(r) = 3 \,cm$Height $(h) = 10.5 \,cm$Surface area of $1$ penholder $= 2\pi rh + \pi r^2 = \pi r(2h + r)$$= \frac{22}{7} \times 3 \times (2 \times 10.5 + 3) \,cm^2$$= \frac{22}{7} \times 3 \times (21 + 3) \,cm^2$$= \frac{22}{7} \times 3 \times 24 \,cm^2 = \frac{1584}{7} \,cm^2$Total cardboard required for $35$ competitors $= 35 \times \left(\frac{1584}{7}\right) \,cm^2$$= 5 \times 1584 \,cm^2 = 7920 \,cm^2$Thus,$7920 \,cm^2$ of cardboard is required.

Class 9 Mathematics Surface Areas and Volumes Textbook - Surface Areas and Volumes

Difficult

The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base,using cardboard. Each penholder was to be of radius $3 \,cm$ and height $10.5 \,cm$. The Vidyalaya was to supply the competitors with cardboard. If there were $35$ competitors,how much cardboard was required to be bought for the competition (in $,cm^2$)? $\left[\text{Assume } \pi = \frac{22}{7}\right]$

A
$1120$
B
$8560$
C
$9920$
D
$7920$

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Class 9 Questions

Class 9

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Surface Areas and Volumes

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Textbook - Surface Areas and Volumes

$A$ river $3 \,m$ deep and $40 \,m$ wide is flowing at the rate of $2 \,km$ per hour. How much water will fall into the sea in a minute (in $,m^3$)?

Medium

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Find the surface area of a sphere with a diameter of $3.5 \, cm$. Assume $\pi = \frac{22}{7}$. (in $, cm^2$)

Easy

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Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions $25 \,cm \times 20 \,cm \times 5 \,cm$ and the smaller of dimensions $15 \,cm \times 12 \,cm \times 5 \,cm$. For all the overlaps,$5\%$ of the total surface area is required extra. If the cost of the cardboard is $Rs. 4$ for $1000 \,cm^2$,find the cost of cardboard required for supplying $250$ boxes of each kind.

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$A$ matchbox measures $4 \,cm \times 2.5 \,cm \times 1.5 \,cm.$ What will be the volume of a packet containing $12$ such boxes (in $,cm^3$)?

Easy

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$A$ village,having a population of $4000$,requires $150$ litres of water per head per day. It has a tank measuring $20 \,m \times 15 \,m \times 6 \,m$. For how many days will the water of this tank last?

Medium

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$A$ river $3 \,m$ deep and $40 \,m$ wide is flowing at the rate of $2 \,km$ per hour. How much water will fall into the sea in a minute (in $,m^3$)?

Find the surface area of a sphere with a diameter of $3.5 \, cm$. Assume $\pi = \frac{22}{7}$. (in $, cm^2$)

$A$ matchbox measures $4 \,cm \times 2.5 \,cm \times 1.5 \,cm.$ What will be the volume of a packet containing $12$ such boxes (in $,cm^3$)?

$A$ village,having a population of $4000$,requires $150$ litres of water per head per day. It has a tank measuring $20 \,m \times 15 \,m \times 6 \,m$. For how many days will the water of this tank last?

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