Question

find the volume and TSA of a cone having radius 3cm and height 4cm with full explanation?​

Answer 1

Answer:

$volume = 12\pi \: {cm}^{3} \\ tsa = 24\pi \: {cm}^{2} .$

Step-by-step explanation:

$volume = \frac{1}{3} \times \pi {r}^{2} h = \frac{1}{3 } \times \pi \times {3}^{2} \times 4 = 12\pi \: {cm}^{3} \\ \\ l = \sqrt{ {3}^{2} + {4}^{2} } = 5 \: cm \\ \\ tsa = \pi \: r \:( r + \: l) \\ \\ tsa= \pi \: (3)(3 + 5) = 24\pi \: {cm}^{2} .$

Answer 2

$\huge\underline\mathtt\color{teal}Given$

• Radius of the cone = 3 cm
• Height of the cone = 4 cm.

$\huge\underline\mathtt\color{teal}To \: find$

• The volume and TSA of the cone.

$\huge\underline\mathtt\color{teal}Solution$

We know that,

$\sf{</u></strong><strong><u>T</u></strong><strong><u>he \: volume \: of \: the \: cone = \frac{1}{3} \pi {r}^{2} h}$

$\sf{</u></strong><strong><u>T</u></strong><strong><u>he \: volume \: of \: the \: cone = \frac{1}{3} \times \frac{22}{7} \times ({3})^{2} \times 4}$

$\sf{</u></strong><strong><u>T</u></strong><strong><u>he \: volume \: of \: the \: cone = \frac{1}{\cancel3} \times \frac{22}{7} \times {\cancel 3} \times 3 \times 4}$

$\sf{</u></strong><strong><u>T</u></strong><strong><u>he \: volume \: of \: the \: cone = \frac{264}{7} }$

$\sf{</u></strong><strong><u>T</u></strong><strong><u>he \: volume \: of \: the \: cone = 37.71}$

Now,

$\sf{{l}^{2} = {r}^{2} + {h}^{2} }$

$\sf{\implies l = \sqrt{ {r}^{2} + {h}^{2} } }$

Now ,putting the values,we get,

$\sf{\implies l = \sqrt{ {3}^{2} + {4}^{2} } }$

$\sf{\implies l = \sqrt{9 + 16} }$

$\sf{\implies l = \sqrt{25}}$

$\sf{\implies l = 5</u></strong><strong><u> </u></strong><strong><u>cm</u></strong><strong><u>}$

Again,we know that,

The total surface area of the cone

$\sf{ = \pi \: r(r + l)}$

$\sf{\implies \: </u></strong><strong><u>TSA</u></strong><strong><u> </u></strong><strong><u>= \frac{22}{7} \times 3(3 + 5)}$

$\sf{\implies </u></strong><strong><u>TSA</u></strong><strong><u> </u></strong><strong><u>= \frac{66}{7} \times 8 }$

$\sf{\implies </u></strong><strong><u>TSA</u></strong><strong><u> </u></strong><strong><u>= 75.42 }$

"Hence, the volume of the cone=37.71 cm³ and the total surface area of the cone = 75.42 sq.cm"