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Volumes Practice Test 3

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Question : 36 of 40

Marks: +1, -0

A solid is in the form of a right circular cylinder with hemispherical ends. The total length of the solid is 35 cm. The diameter of the cylinder is ¼ th of its height. Find the volume and total surface area of the solid.

(Use π = 22/7)

1050.67 $\mathrm{cm}^3$ ; 750 $\mathrm{cm}^2$
1150.67 $\mathrm{cm}^3$ ; 760 $\mathrm{cm}^2$
1250.67 $\mathrm{cm}^3$ ; 765 $\mathrm{cm}^2$
1257.67 $\mathrm{cm}^3$ ; 770 $\mathrm{cm}^2$

Solution:

Here,

\frac{h}{4}

= 2r

∴ h = 8r

Since, 8r + r + r = 35

∴ r =

\frac{35}{10}

= 3.5 cm and also, h = 8 × 3.5 = 28 cm

Volume of whole solid =

\pi r^2 h + 2 \times \frac{2}{3} \pi r^3

=

\frac{22}{7} \times (3.5)^2 \left[28 + \frac{4}{3} \times 3.5\right]

=

38.5 \times \frac{98}{3}

=

\frac{3773}{3}

= 1257.67

\mathrm{cm}^3

Total surface area of the solid =

2\pi r h + 2 \times 2\pi r^2

= 2πr (h + 2r)

=

2 \times \frac{22}{7} \times 3.5

(28 + 2 × 3.5)

= 22 × 35 = 770

\mathrm{cm}^2

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